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1. State the limitations in measuring Z, Y and ABCD parameters at microwave frequencies. [N/D – 11] The limitations in measuring Z, Y and ABCD parameters at microwave frequencies are, i. Equipment is not readily available to measure total voltage and current at the ports of the network. ii. Short circuit and open circuit are difficult to achieve over a wide range of frequencies. iii. Presence of active devices such as power transistors and tunnel diodes makes the circuit unstable. 2. Specify the X-band frequency range and wavelength. The X-band frequency range
: 8 – 12.5 GHz
The X-band wavelength
: 3.75 cm – 2.4 cm
3. Specify the ABCD relationship of a lossless transmission line.
[N/D – 07]
[N/D – 05]
The ABCD relationship of a lossless transmission line is, V1= AV2 - BI2 I1 = CV2 - DI2 Where, V1 – voltage at port 1 I1 – current at port 1 V2 – voltage at port 2 I2 – current at port 2 4. Specify the K-band frequency range and wavelength. The K-band frequency range
: 18 – 26.5 GHz
The K-band wavelength
: 1.67 – 1.13 cm
[M/J – 07]
5. A 5dB attenuator is specified as having voltage standing wave ratio (VSWR) of 1.2. Assuming the device is reciprocal, find the S parameters. [N/D – 11] |S21| = |S12|= 0 |S11| or |S22|= (VSWR-1) / (VSWR+1) |S11| or |S22|= (1.2-1)/ (1.2+1) |S11| or |S22|= 0.09
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6. What is meant by symmetry of scattering matrix?
[M/J – 08]
|S| is a symmetric matrix when the microwave device has the same transmission characteristics in either direction of a pair of ports. Sij = Sji 7. State the properties of S parameter.
[N/D – 12]
The properties of S parameter are, i. |S| is always a square matrix of order (n*n) ii. |S| is a symmetric matrix iii. |S| is a unitary matrix iv. Under perfect matched conditions, the diagonal elements of |S| are zero 8. Draw the equivalent circuit of a practical capacitor.
[N/D – 12]
9. List the radio,frequency bands available in microwave and radio frequency ranges. [N/D-16] Band Number 4
Abbreviation VLF
Frequency Range 3 to 30 kHz
Wavelength Range† 10 to 100 km
5
LF
30 to 300 kHz
1 to 10 km
6
MF
300 to 3000 kHz
100 to 1000 m
7
HF
3 to 30 MHz
10 to 100 m
8
VHF
30 to 300 MHz
1 to 10 m
9 10
UHF SHF
300 to 3000 MHz 3 to 30 GHz
10 to 100 cm 1 to 10 cm
11
EHF
30 to 300 GHz
1 to 10 mm
12
THF
300 to 3000 GHz
0.1 to 1 mm
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10. Define S-Parameters. [N/D-16] Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals.
11. Define − Skin Effect As frequency increases, the electrical signals propagate less inside the conductor. Because of the current density increases to the perimeter of the wire and causes higher impedance for the signal. This effect is known as skin effect. 12. State the different types of high frequency capacitors. The different types of high frequency capacitors are, i. Parallel plate capacitor ii. Leaded capacitor iii. Perfect capacitor 13. State the different types of high frequency resistors. The different types of high frequency resistors are, i. Carbon composite resistors ii. Metal film resistors iii. Thin-film chip resistors 14. State the different types of high frequency inductors. The different types of high frequency inductors are, i. Simple wire inductor ii. Coiled wire inductor
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Part – B 1. What is transmission (T) matrix? Obtain and explain the relationship with [S]and viceversa. (8) 2. Write the ABCD matrix for a two-port network and derive its S matrix.
[N/D-16]
(8) [N/D – 12]
ABCD parameters or the transmission line parameters provide the link between the supply and receiving end voltages and currents, considering the circuit elements to be linear in nature. Thus the relation between the sending and receiving end specifications are given using ABCD parameters by the equations below.
Now in order to determine the ABCD parameters of transmission line let us impose the required circuit conditions in different cases. ABCD Parameters, When Receiving End is Open Circuited
The receiving end is open circuited meaning receiving end current IR = 0.
Applying this condition to equation (1) we get
, Thus its implies that on applying open circuit condition to ABCD parameters, we get parameter A as the ratio of sending end voltage to the open circuit receiving end voltage. Since dimension wise A is a ratio of voltage to voltage, A is a dimension less parameter.
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Applying the same open circuit condition i.e IR = 0 to equation (2)
Thus its implies that on applying open circuit condition to ABCD parameters of transmission line, we get parameter C as the ratio of sending end current to the open circuit receiving end voltage. Since dimension wise C is a ratio of current to voltage, its unit is mho. Thus C is the open circuit conductance and is given by C = IS ⁄ VR mho. ABCD Parameters, When Receiving End is Short Circuited
Receiving end is short circuited meaning receiving end voltage VR = 0 Applying this condition to equation (1) we get,
Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter B as the ratio of sending end voltage to the short circuit receiving end current. Since dimension wise B is a ratio of voltage to current, its unit is Ω. Thus B is the short circuit resistance and is given by B = VS ⁄ IR Ω. Applying the same short circuit condition i.e VR = 0 to equation (2) we get
Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter D as the ratio of sending end current to the short circuit receiving end current. Since dimension wise D is a ratio of current to current, it’s a dimension less parameter. Visit : www.EasyEngineeering.net
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3. Explain in detail, the properties of S parameters.
(8) [N/D – 11]
4. Explain the properties of S-matrix and derive the S-matrix representation of n-port network. (8) [M/J – 12] PROPERTIES OF S-PARAMETER 1) Zero diagonal elements for perfect matched network For an ideal network with matched termination Sii=0, since there is no refiection from any port. Therefore under perfect matched condition yhe diagonal element of [s] are zero 2) Symmetry of [s] for a reciprocal network The reciprocal device has a same transmission characteristics in either direction of a pair of ports and is characterized by a symmetric scattering matrix Sij = Sji ; i≠j Which results [S] t = [S] For a reciprocal network with assumed normalized the impeadence matrix equation is [b] = ( [z] + [u] )-1 ([z] – [u]) [a] -----------(1) Where u is the unit matrix S matrix equation of network is [b] = [s] [a] ------------(2) Compare equ (1) & (2) [s] =([z]+[u])-1 ([z] – [u]) [R] = [Z] – [U] [Q] = [Z] + [U] For a reciprocal network Z matrix Symmetric [R] [Q] = [Q] [R] [Q] -1[R][Q][Q]-1 = [Q]-1[Q][R][Q]-1 [Q] -1[R] = [R][Q]-1 [Q] -1[R] [ S ] = [R][Q]-1 ------------(3) [S]t = [Z-u]t [ Z+U]t -1 Then [Z-u]t = [ Z-U] [Z+u]t -1 = [ Z+U] Visit : www.EasyEngineeering.net
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[S] t = [z-u] [z+u]-1 [S] t = [R][Q]-1 -------------(4) When compare 3 & 4 [S] t = [S] 3) Unitary property of lossless network For any loss less network the sum of product of each term of any one row or any one column of s matrix multiplied by its complex conjugate is unity For a lossless N port devices the total power leaving N ports must be equal to total input to the ports 4) Zero property It states that the sum of the product of any each term of any one row or any one column of a s matrix is multiplied by the complex conjucate of corresponding terms of any other row is zero
5. A shunt impedance Z is connected across a transmission line characteristic impedance Z0. Calculate the S matrix of the junction. (8) [N/D – 11] A Z-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports. A port in this context is a pair of electrical terminals carrying equal and opposite currents into and out-of the network, and having a particular voltage between them. The Z-matrix gives no information about the behaviour of the network when the currents at any port are not balanced in this way (should this be possible), nor does it give any information about the voltage between terminals not belonging to the same port. Typically, it is intended that each external connection to the network is between the terminals of just one port, so that these limitations are appropriate. For a generic multi-port network definition, it is assumed that each of the ports is allocated an integer n ranging from 1 to N, where N is the total number of ports. For port n, the associated Z-parameter definition is in terms of the port For all ports the voltages may be defined in terms of the Z-parameter matrix and the currents by the following matrix equation: V =Z * I where Z is an N × N matrix the elements of which can be indexed using conventional matrix notation. In general the elements of the Z-parameter matrix are complex numbers and functions of frequency. For a one-port network, the Zmatrix reduces to a single element, being the ordinary impedance measured between the two terminals.The Zparameters are also known as the open circuit parameters because they are measured or calculated by applying current to one port and determining the resulting voltages at all the ports while the undriven ports are terminated into an open circuits.
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DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING EC6701 – RF AND MICROWAVE ENGINEERING
UNIT 2 PART A
1. What is meant by power gain of an amplifier? [N/D – 12] Transducer power gain is defined as the ratio of power delivered to the load to that of the power from the source. 2. Write the expression for noise figure of a two port amplifier. [N/D – 11] The expression for noise figure of a two port amplifier is F = Fmin + (Gn/Rs) |Zs – Zopt|2 Where, F – Noise figure Fmin – Minimum noise figure Gn – Source conductance Rs – Source resistance Zs – Source impedance Zopt – Optimum impedance 3. What is the need for impedance matching network? [N/D – 11] The need for impedance matching network is, i. To stabilize the amplifier by keeping the source and load impedances in the appropriate range ii. To reduce undesired reflections iii. To improve the power flow capabilities 4. What are the considerations in selecting a matching network? The considerations in selecting a matching network are, i. Gain and gain flatness ii. Operating frequency and bandwidth iii. Output power iv. Power supply requirements v. Input and output reflection coefficients vi. Noise figure 5. Define − Noise Figure Noise figure is defined as the ratio of input SNR to the output SNR. F = (SNR) O / (SNR) I
[N/D – 12]
[N/D-16]
6. Calculate VSWR of an amplifier, if the amplifier has reflection coefficient 0.2533.[N/D-16] VSWR = (1 + R.C)/(1-R.C) VSWR = (1+0.2533)/(1-0.2533) VSWR = 1.678
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7. Define − Unilateral Power Gain When feedback effect of the amplifier is neglected (i.e. S12 = 0), the amplifier power gain is known as unilateral power gain. 8. Define − Operating Power Gain Operating power gain is defined as the power delivered to the load to that of the power supplied to the amplifier. 9. Define − Available Power Gain Available power gain is defined as the power available from the microwave network to that of the power from the source. 10. State the various types of waveguide stub. The various types of waveguide stub are, i. E stub ii. H stub iii. E-H tuner 11. Define – Positive RF Feedback. Positive feedback is defined as the instability caused due to the increase in the magnitude of the return voltage in a passive radio frequency waveguide.
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Dhanalakshmi College of Engineering Department of ECE EC6701 – RF and Microwave Engineering Unit 3 1. Draw the diagram of H-plane Tee junction.
[N/D – 12]
2. Draw the structure of two hole directional coupler.
3. What is meant by directivity of directional coupler?
[N/D – 11]
[M/J – 08]
The directivity of directional coupler is defined as the ratio of forward power Pr to f the back power Pb and expressed in dB. 4. What are the basic parameters to measure the performance of a directional coupler?
[N/D – 08]
The basic parameters to measure the performance of a directional coupler are, i. Coupling co-efficient ii. Directivity iii. Insertion loss iv. Isolation 5. What are the basic types of directional coupler?
[N/D – 09]
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ii. Four hole directional coupler iii. Reverse coupling directional coupler iv. Bethe hole directional coupler 6. How a Faraday rotation isolator can be constructed by using ferrite rod?
[N/D – 08]
Isolators can be made by inserting ferrite rod along the axis of a rectangular waveguide. 7. State the significance of Rat-race junctions.
[M/J - 13]
i. easy to realize in planar technologies such as microstrip and stripline ii. a rat-race needs no matching structure to achieve correct operation. iii. Rat-race couplers are used to sum two in-phase combined signals with essentially no loss iv. It equally split an input signal with no resultant phase difference between its outputs.
8. What is gyrator?
[N/D – 13]
A gyrator is a passive, linear, lossless, two-port ferrite device. An ideal gyrator is a linear two port device which generate relative phase shift of 180 degree in forward direction zero degree phase shift in reverse direction.
9. State the applications of gyrator and isolator.
[N/D – 14]
A gyrator is a nonreciprocal electrical network. It is capable of transforming signals or energy represented in terms of one electrical quantity, such as voltage or magnetic field, to another electrical quantity, such as current or electric field. An isolator is a two-port device that transmits microwave or radio frequency power in one direction only. It is used to shield equipment on its input side, from the effects of conditions on its output side; for example, to prevent a microwave source being detuned by a mismatched load. 10. State transferred electron effect.
[N/D – 12]
When GaAs is biased above a threshold value of the electric field, it exhibits a negative differential mobility. The electrons in the lower energy band will be transferred into the higher energy band. This behavior is called transferred electron effect.
11. State Gunn Effect.
[M/J – 08] [M/J – 13]
When the electric field is varied from zero to threshold value, the carrier drift velocity is increased from zero to maximum. When the electric field is beyond the threshold value of 3000V/cm, the drift velocity is decreased and the diode exhibits negative resistance. Visit : www.EasyEngineeering.net
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12. What are the major disadvantages of IMPATT diodes?
[N/D – 08]
The major disadvantages of IMPATT diodes are, i. Avalanche process makes the IMPATT diode noisy ii. Poor noise figure of 30dB iii. Low efficiency due to induced electron current 13. State the basic materials required for microwave integrated circuit.
[N/D – 07]
The basic materials required for microwave integrated circuit are, i. Substrate materials ii. Conductor materials iii. Dielectric materials iv. Resistive materials 14. State the different types of lithography.
[M/J – 08]
The different types of lithography are, i. Electron-beam lithography ii. Ion-beam lithography iii. Optical lithography iv. X-ray lithography
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1. Explain the working principle of E plane tee and derive its S parameters. [N/D - 15] 2. Discuss the properties of scattering matrix. Determine the S matrix representation of E plane tee junction. [N/D - 14] Visit[A/M : www.EasyEngineeering.net 3. Explain the properties of E plane tee. - 13]
Microwave Engineering - E-Plane Tee
An E-Plane Tee junction is formed by attaching a simple waveguide to the broader dimension of a rectangular waveguide, which already has two ports. The arms of rectangular waveguides make two ports called collinear ports i.e., Port1 and Port2, while the new one, Port3 is called as Side arm or E-arm. T his E-plane Tee is also called as Series Tee. As the axis of the side arm is parallel to the electric field, this junction is called E-Plane Tee junction. This is also called as Voltage or Series junction. The ports 1 and 2 are 180° out of phase with each other. The cross-sectional details of E-plane tee can be understood by the following figure.
The following figure shows the connection made by the sidearm to the bi-directional waveguide to form the parallel port.
Properties of E-Plane Tee The properties of E-Plane Tee can be defined by its
[S ]3x3
matrix.
It is a 3×3 matrix as there are 3 possible inputs and 3 possible outputs. S 11
S 12
S 13
[S ] = ⎢ S 21
S 22
S 23 ⎥
S 32
S 33
⎡
⎣
Scattering coefficients
S 13
and
S 23
S 31
⎤
........ Equation 1
⎦
are out of phase by 180° with an input at port 3. S 23 = −S 13
........ Equation 2
The port is perfectly matched to the junction. S 33 = 0
........ Equation 3
From the symmetric property,
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Visit : Microwave www.EasyEngineeering.net Engineering E Plane Tee S ij = S ji
........ Equation 4
S 12 = S 21 S 23 = S 32 S 13 = S 31
Considering equations 3 & 4, the
[S ]
matrix can be written as, S 11
S 12
[S ] = ⎢ S 12
S 22
⎡
⎣
S 13
S 13
⎤
........ Equation 5
−S 13 ⎥
−S 13
⎦
0
We can say that we have four unknowns, considering the symmetry property. From the Unitary property [S ][S ]∗ = [I ]
S 11
S 12
⎢ S 12
S 22
⎡
⎣
S 13
S 13
S
⎤ ⎡
∗
S
11
∗ −S 13 ⎥ ⎢ ⎢ S 12 ⎦ ⎣ ∗ 0 S
−S 13
S
∗
∗
∗ 13
−S
22
−S
13
S
12
∗
∗ 13
0
13
1
0
0
⎥ = ⎢0 ⎥ ⎣ ⎦ 0
1
0⎥
0
1
⎤
⎡
⎤
⎦
Multiplying we get, (Noting R as row and C as column) R1 C 1 : S 11 S
∗ 11
+ S 12 S
∗ 12
|S 11 |
R2 C 2 : |S 12 |
2
2
+ S 13 S
∗
+ |S 11 |
+ |S 22 |
2
= 1
13
2
+ |S 11 |
+ |S 13 |
R3 C 3 : |S 13 |
R3 C 1 : S 13 S
∗ 11
2
2
2
......... Equation 7
= 1
+ |S 13 |
− S 13 S
........ Equation 6
= 1
2
∗ 12
......... Equation 8
= 1
......... Equation 9
= 1
Equating the equations 6 & 7, we get ......... Equation 10
S 11 = S 22
From Equation 8, 2|S 13 |
2
or
......... Equation 11
1
S 13 =
√2
From Equation 9, S 13 (S
Or
∗ 11
− S
∗ 12
)
......... Equation 12
S 11 = S 12 = S 22
Using the equations 10, 11, and 12 in the equation 6, we get, |S 11 |
2
+ |S 11 |
2
+
1 2
= 1
2|S 11 |
Or Substituting the values from the above equations in
[S ]
2
=
S 11 =
1 2
......... Equation 13
1 2
matrix,
We get, ⎡ ⎢ [S ] = ⎢ ⎢ ⎢ ⎣
We know that
[b]
=
1
1
1
2
2
√2
1
1
2
2
1 2
−
− 1
1 √2
⎥ ⎥ ⎥ ⎥ ⎦
0
√2
⎤
[S ][a]
1
⎡
1
1
⎤
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b1
⎢ b2 ⎣
b3
⎡ ⎤
⎢ ⎢ ⎥ = ⎢ ⎢ ⎦ ⎣
1
1
1
2
2
√2
1
1
2 1 2
−
2
−
1 √2
1 √2
0
⎤
a ⎡ 1⎤ ⎥ ⎥ ⎥ ⎢ a2 ⎥ ⎥⎣ ⎦ a3 ⎦
This is the scattering matrix for E-Plane Tee, which explains its scattering properties.
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3/3
4. 5. 6.
Visit : www.EasyEngineeering.net Draw and explain the operation of magic tee. Explain its application in the construction of a 4 port circulator. Describe magic tee with neat sketch. [N/D - 13] Explain the properties of magic tee and derive scattering matrix for it.
Microwave Engineering - E-H Plane Tee
An E-H Plane Tee junction is formed by attaching two simple waveguides one parallel and the other series, to a rectangular waveguide which already has two ports. This is also called as Magic Tee, or Hybrid or 3dB coupler. The arms of rectangular waveguides make two ports called collinear ports i.e., Port 1 and Port 2, while the Port 3 is called as H-Arm or Sum port or Parallel port. Port 4 is called as E-Arm or Difference port or Series port. The cross-sectional details of Magic Tee can be understood by the following figure.
The following figure shows the connection made by the side arms to the bi-directional waveguide to form both parallel and serial ports.
Characteristics of E-H Plane Tee If a signal of equal phase and magnitude is sent to port 1 and port 2, then the output at port 4 is zero and the output at port 3 will be the additive of both the ports 1 and 2. If a signal is sent to port 4, (E-arm) then the power is divided between port 1 and 2 equally but in opposite phase, while there would be no output at port 3. Hence,
S 34
= 0.
If a signal is fed at port 3, then the power is divided between port 1 and 2 equally, while there would be no output at port 4. Hence,
S 43
= 0.
If a signal is fed at one of the collinear ports, then there appears no output at the other collinear port, as the E-arm produces a phase delay and the H-arm produces a phase advance. So,
S 12
=
S 21
= 0.
Properties of E-H Plane Tee The properties of E-H Plane Tee can be defined by its
[S ]
4×4
matrix.
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It is a 4×4 matrix as there are 4 possible inputs and 4 possible outputs. S 11
S 12
S 13
S 14
⎢ S 21 [S ] = ⎢ ⎢S 31
S 22
S 23
S 32
S 33
S 24 ⎥ ⎥ ⎥ S
S 42
S 43
S 44
⎡
⎣
S 41
⎤
........ Equation 1
34
⎦
As it has H-Plane Tee section ........ Equation 2
S 23 = S 13
As it has E-Plane Tee section ........ Equation 3
S 24 = −S 14
The E-Arm port and H-Arm port are so isolated that the other won't deliver an output, if an input is applied at one of them. Hence, this can be noted as ........ Equation 4
S 34 = S 43 = 0
From the symmetry property, we have S ij = S ji
S 12 = S 21 , S 13 = S 31 , S 14 = S 41
........ Equation 5
S 23 = S 32 , S 24 = S 42 , S 34 = S 43
If the ports 3 and 4 are perfectly matched to the junction, then ........ Equation 6
S 33 = S 44 = 0
Substituting all the above equations in equation 1, to obtain the S 11
S 12
S 13
⎢ S 12 [S ] = ⎢ ⎢S 13
S 22
S 13
S 13
0
−S 14
0
⎡
⎣
From Unitary property, S 11
S 12
S 13
⎢ S 12 ⎢ ⎢S 13
S 22
S 13
S 13
0
−S 14
0
⎡
⎣
S 14
∗
[S ][S ]
S 14
0
1
0
0
0
⎢0 = ⎢ ⎢0
1
0
0
1
0 ⎥ ⎥ 0 ⎥
0
0
1
⎡
⎣
0
R1 C 1 : |S 11 |
R2 C 2 : |S 12 |
R3 C 3 : |S 13 |
R4 C 4 : |S 14 |
2
2
2
2
matrix,
⎤
−S 14 ⎥ ⎥ ⎥ 0
........ Equation 7
⎦
0
= [I ]
⎤⎡
−S 14 ⎥ ⎥ ⎥ 0
S 14
S 14
[S ]
S
∗
S
11 ∗
⎢S 12 ⎢ ⎢ ⎢ S 13
⎦⎣
S 14
S
∗ 12 ∗ 22
S S
∗ 13 ∗ 13
S
∗ 14
⎤
∗
⎥ ⎥ ⎥ ⎥
−S
S 13
0
0
−S 14
0
0
14
⎦
⎤
⎦
+ |S 12 |
+ |S 22 |
+ |S 13 |
+ |S 14 |
2
2
2
2
+ |S 13 |
+ |S 13 |
2
2
= 1 + |S 14 |
= 1 + |S 14 |
2
2
= 1
......... Equation 8
= 1
......... Equation 9
= 1
......... Equation 10
= 1
......... Equation 11
From the equations 10 and 11, we get S 13 =
S 14 =
1 √2
1 √2
........ Equation 12 ........ Equation 13
Comparing the equations 8 and 9, we have S 11 = S 22
......... Equation 14
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Using these values from the equations 12 and 13, we get |S 11 |
2
+ |S 12 |
2
+
1 2
1
+
|S 11 |
2
2
= 1
+ |S 12 |
2
= 0
......... Equation 15
S 11 = S 22 = 0
From equation 9, we get
......... Equation 16
S 22 = 0
Now we understand that ports 1 and 2 are perfectly matched to the junction. As this is a 4 port junction, whenever two ports are perfectly matched, the other two ports are also perfectly matched to the junction. The junction where all the four ports are perfectly matched is called as Magic Tee Junction. By substituting the equations from 12 to 16, in the
[S ]
matrix of equation 7, we obtain the scattering matrix of Magic Tee as 0
⎡ ⎢ ⎢ ⎢ [S ] = ⎢ ⎢ ⎢ ⎢
0 1
1 √2
1 √2
[b]
=
0
√2
⎣
We already know that,
0
−
1
1
2
√2
1
1
2
1 √2
−
√2
0
0
0
0
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
[S ][a]
Rewriting the above, we get
∣ b1 ∣ ∣
∣ b2 ∣ ∣
b3
∣ b4
⎡
⎢ ∣ ⎢ ⎢ ∣ = ⎢ ∣ ⎢ ⎢ ∣ ⎢ ∣ ⎣
0
0
0
0
1
1
√2
√2
1 √2
−
1 √2
1
1
2
√2
1
1
2
−
√2
0
0
0
0
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
∣ a1 ∣ ∣
∣ ∣ a2 ∣ ∣ ∣
a3
∣ ∣
∣ a4 ∣
Applications of E-H Plane Tee Some of the most common applications of E-H Plane Tee are as follows − E-H Plane junction is used to measure the impedance − A null detector is connected to E-Arm port while the Microwave source is connected to H-Arm port. The collinear ports together with these ports make a bridge and the impedance measurement is done by balancing the bridge. E-H Plane Tee is used as a duplexer − A duplexer is a circuit which works as both the transmitter and the receiver, using a single antenna for both purposes. Port 1 and 2 are used as receiver and transmitter where they are isolated and hence will not interfere. Antenna is connected to E-Arm port. A matched load is connected to H-Arm port, which provides no reflections. Now, there exists transmission or reception without any problem. E-H Plane Tee is used as a mixer − E-Arm port is connected with antenna and the H-Arm port is connected with local oscillator. Port 2 has a matched load which has no reflections and port 1 has the mixer circuit, which gets half of the signal power and half of the oscillator power to produce IF frequency. In addition to the above applications, an E-H Plane Tee junction is also used as Microwave bridge, Microwave discriminator, etc.
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Visit : www.EasyEngineeering.net 7. Explain the concept of two-hole directional coupler and derive its S – matrix. [A/M - 12] 8. Explain how directional coupler can be used to measure reflected power. [N/D - 12] 9. Derive the expression for directional coupler. [A/M - 13] 10. Describe directional coupler with neat sketch. [N/D - 13]
Microwave Engineering - Directional Couplers
A Directional coupler is a device that samples a small amount of Microwave power for measurement purposes. The power measurements include incident power, reflected power, VSWR values, etc. Directional Coupler is a 4-port waveguide junction consisting of a primary main waveguide and a secondary auxiliary waveguide. The following figure shows the image of a directional coupler.
Directional coupler is used to couple the Microwave power which may be unidirectional or bi-directional.
Properties of Directional Couplers The properties of an ideal directional coupler are as follows. All the terminations are matched to the ports. When the power travels from Port 1 to Port 2, some portion of it gets coupled to Port 4 but not to Port 3. As it is also a bi-directional coupler, when the power travels from Port 2 to Port 1, some portion of it gets coupled to Port 3 but not to Port 4. If the power is incident through Port 3, a portion of it is coupled to Port 2, but not to Port 1. If the power is incident through Port 4, a portion of it is coupled to Port 1, but not to Port 2. Port 1 and 3 are decoupled as are Port 2 and Port 4. Ideally, the output of Port 3 should be zero. However, practically, a small amount of power called back power is observed at Port 3. The following figure indicates the power flow in a directional coupler.
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Where Pi
= Incident power at Port 1
Pr
= Received power at Port 2
Pf
= Forward coupled power at Port 4
Pb
= Back power at Port 3
Following are the parameters used to define the performance of a directional coupler.
Coupling Factor (C) The Coupling factor of a directional coupler is the ratio of incident power to the forward power, measured in dB. C = 10 log10
Pi
dB
Pf
Directivity (D) The Directivity of a directional coupler is the ratio of forward power to the back power, measured in dB. Pf D = 10 log10
dB Pb
Isolation It defines the directive properties of a directional coupler. It is the ratio of incident power to the back power, measured in dB. I = 10 log10
Pi
dB
Pb
Isolation in dB = Coupling factor + Directivity
Two-Hole Directional Coupler This is a directional coupler with same main and auxiliary waveguides, but with two small holes that are common between them. These holes are
λg /4
distance apart where λg is the guide wavelength. The following figure shows the image of a two-hole directional coupler.
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A two-hole directional coupler is designed to meet the ideal requirement of directional coupler, which is to avoid back power. Some of the power while travelling between Port 1 and Port 2, escapes through the holes 1 and 2. The magnitude of the power depends upon the dimensions of the holes. This leakage power at both the holes are in phase at hole 2, adding up the power contributing to the forward power Pf. However, it is out of phase at hole 1, cancelling each other and preventing the back power to occur. Hence, the directivity of a directional coupler improves.
Waveguide Joints As a waveguide system cannot be built in a single piece always, sometimes it is necessary to join different waveguides. This joining must be carefully done to prevent problems such as − Reflection effects, creation of standing waves, and increasing the attenuation, etc. The waveguide joints besides avoiding irregularities, should also take care of E and H field patterns by not affecting them. There are many types of waveguide joints such as bolted flange, flange joint, choke joint, etc.
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Fatima Michael College of Engineering & Technology Visit : www.EasyEngineeering.net 12. Explain the working principle of GUNN diode and its mode. [N/D - 15] 13. Explain the working principle of GUNN diode using two valley theory. [A/M-15] 14. Explain the operating principle of GUNN diode. [A/M - 14]
i)Voltage-controlled and ii) current controlled modes as shown in Fig.
In the voltage-controlled mode the current density can be multivalued, whereas in the current-controlled mode the voltage can be multivalued.
The major effect of the appearance of a differential negative-resistance region in the currentdensityfield curve is to render the sample electrically unstable. As a result, the initially homogeneous sample becomes electrically heterogeneous in an attempt to reach stability. In the voltage-controlled negative-resistance mode high-field domains are formed, separating two lowfield regions. The interfaces separating lowand high-field domains lie along equipotentials; thus they are in planes perpendicular to the current direction as shown in Fig. 7-2-2(a). In the currentcontrolled negative-resistance mode splitting the sample results in high-current filaments running along the field direction as shown in Fig. 7-2-2(b).
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Expressed mathematically, the negative resistance of the sample at a particular region is
If an electric field Eo (or voltage Vo) is applied to the sample, for example, the current density is generated. As the applied field (or voltage) is increased to E2 (or V2), the current density is decreased to J2. When the field (or voltage) is decreased to E1 (or V1), the current density is increased to J1 . These phenomena of the voltage controlled negative resistance are shown in Fig. 7-2-3(a). Similarly, for the current controlled mode, the negative-resistance profile is as shown in Fig. 7-2-3(b).
Two-Valley Model Theory According to the energy band theory of then-type GaAs, a high-mobility lower valley is separated by an energy of 0.36 eV from a low-mobility upper valley
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When the applied electric field is lower than the electric field of the lower valley (£ < Ec), no electrons will transfer to the upper valley as show in Fig. 7-2-S(a).
When the applied electric field is higher than that of the lower valley and lower than that of the upper valley (Ec < E < Eu), electrons will begin to transfer to the upper valley as shown in Fig. 7-2-S(b).
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And when the applied electric field is higher than that of the upper valley (Eu < E), all electrons will transfer to the upper valley as shown in Fig. 7-2-S(c).
If electron densities in the lower and upper valleys are nc and nu , the conductivity of the n -type GaAs is
When a sufficiently high field E is applied to the specimen, electrons are accelerated and their effective temperature rises above the lattice temperature. Furthermore, the lattice temperature also increases. Thus electron density n and mobility f-L are both functions of electric field E. Differentiation of Eq. (7-2-2) with respect toE yields
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If the total electron density is given by n = nt + nu and it is assumed that f.Le and /Lu are proportional to EP, where p is a constant, then
Substitution of Eqs. (7-2-4) to (7-2-6) into Eq. (7-2-3) results in
Then differentiation of Ohm's law J = aE with respect toE yields
Equation (7-2-8) can be rewritten
Clearly, for negative resistance, the current density J must decrease with increasing field E or the ratio of dJ!dE must be negative. Such would be the case only if the right-hand term of Eq. (7-2-9) is less than zero. In other words, the condition for negative resistance is
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Substitution of Eqs. (7-2-2) and (7-2-7) with/= nu/ne results in [2]
4.7 AVALANCE TRANSIT TIME DEVICES: Avalanche transit-time diode oscillators rely on the effect of voltage breakdown across a reversebiased p-n junction to produce a supply of holes and electrons. Ever since the development of modern semiconductor device theory scientists have speculated on whether it is possible to make a two-terminal negative-resistance device. The tunnel diode was the first such device to be realized in practice. Its operation depends on the properties of a forward-biased p-n junction in which both the p and n regions are heavily doped. The other two devices are the transferred electron devices and the avalanche transit-time devices. In this chapter the latter type is discussed. The transferred electron devices or the Gunn oscillators operate simply by the application of a de voltage to a bulk semiconductor. There are no p-n junctions in this device. Its frequency is a function of the load and of the natural frequency of the circuit. The avalanche diode oscillator uses carrier impact ionization and drift in the high-field region of a semiconductor junction to produce a negative resistance at microwave frequencies. The device was originally proposed in a theoretical paper by Read in which he analyzed the negative-resistance properties of an idealized n+p- i-p+ diode. Two distinct modes of avalanche oscillator have been observed. One is the IMPATT mode, which stands for impact ionization avalanche transit-time operation. In this mode the typical dc-to-RF conversion efficiency is 5 to 10%, and frequencies are as high as 100 GHz with silicon diodes. The other mode is the TRAPATT mode, which represents trapped plasma avalanche triggered transit operation. Its typical conversion efficiency is from 20 to 60%. Another type of active microwave device is the BARITT (barrier injected transit-time) diode [2]. It has long drift
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Dhanalakshmi College of Engineering Department of ECE EC6701 – RF and Microwave Engineering Unit 4 Part A 1. What is magnetron? [N/D-16] an electron tube for amplifying or generating microwaves, with the flow of electrons controlled by an external magnetic field. 2. What is Tetrodes and Pentodes? [N/D-16] Tetrode: The tetrode has an fourth electrode added. Called a screen grid, it is normally held at a high potential but lower than that of the anode Pentode: The pentode had a fifth electrode added. Called the suppressor grid, it was held at a low potential to suppress secondary emission 3. What are M-type tubes? [M/J – 08] M type tubes are crossed field devices where the static magnetic field is perpendicular to the electric field. Here the electrons travel in curved path. 4. What is the other name of O-type tube? The other name for O – tube is linear tube or rectilinear beam tube.
[N/D – 07]
5. State any four limitations of conventional tubes at high frequencies. The limitations of conventional tubes at high frequencies are, I. Lead inductance effects
[N/D – 11]
II.
Interelectrode capacitance effects
III.
Transmit angle effects
IV.
Gain bandwidth product limitation
6. A helix travelling wave tube operates at 4 GHz, under a beam voltage of 10 KV and beams current of 500mA. If the helix is 25Ω and interaction length is 20cm, find the gain parameter. [N/D – 11] Given: V0 = 10 kV I0 = 500 mA Z0 = 25 ohm F = 4 GHz L = 20 cm
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Gain parameter C = [I0Z0/4V0]1/3
= 0.068
Vidya of engineering & Technology, Virudhunagar Course Material (Question Bank) 7. WhatSriare the College high frequency effects in conventional tubes? The high frequency effects in conventional tubes are i) Circuit reactance a)Inter electrode capacitance b) Lead inductance ii) Transit time effect iii) Cathode emission iv) Plate heat dissipation area v) Power loss due to skin effect, radiation and dielectric loss.
8. What are the assumptions for calculation of RF power in Reflex Klystron? i) Cavity grids and repeller are plane parallel and very large in extent. ii) No RF field is excited in repeller space ii) Electrons are not intercepted by the cavity anode grid. iv) No debunching takes place in repeller space. iii) The cavity RF gap voltage amplitude V, is small compared to the dc beam voltage VO 9. Give the drawbacks of klystron amplifiers. i) As the oscillator frequency changes then resonator frequency also changes and the feedback path phase shift must be readjusted for a positive feedback. ii) The multicavity klystron amplifiers suffer from the noise caused because bunching is never complete and electrons arrive at random at catcher cavity. Hence it is not used in receivers. 10. What is the effect of transit time? There are two effects. i) At low frequencies, the grid and anode signals are no longer 180O out of phase, thus causing design problems with feedback in oscillators. ii) The grid begins to take power from the driving source and the power is absorbed even when the grid is negatively biased. 11. What are the applications of reflex klystron? i) Signal source in MW generator ii) Local oscillators in receivers iii) It is used in FM oscillator in low power MW links. iv) In parametric amplifier as pump source. 12. What is the purpose of slow wave structures used in TWT amplifiers? Slow wave structures are special circuits that are used in microwave tubes to reduce wave velocity in a certain direction so that the electron beam and the signal wave can interact. In TWT, since the beam can be accelerated only to velocities that are about a fraction of the velocity of light, slow wave structures are used. 13. How are spurious oscillations generated in TWT amplifier? State the method to suppress it. In a TWT, adjacent turns of the helix are so close to each other and hence oscillations are likely to occur. To prevent these spurious signals some form of attenuator is placed near the input end of the tube which absorb the oscillations.
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14. State the applications of TWT. i) Low power, low noise TWT s used in radar and microwave receivers ii) Laboratory instruments iii) Drivers for more powerful tubes iv) Medium and high power CWTWT S are used for communication and radar. 15. Define phase focusing effect. The bunching of electrons in known as “Phase focusing effect” This effect is important because without it, favored electrons will fall behind the phase change of electric field across the gaps. Such electrons are retarded at each interaction with the R.F field in magnetron. 16. What are the advantages of TWT? i) Bandwidth is large. ii) High reliability iii) High gain iv) Constant Performance in space v) Higher duty cycle. 17. What is BWO? State the applications of BWO. A backward wave oscillator (BWO) is microwave cw oscillator with an enormous tuning and ever all frequency coverage range. Applications: i) ii)
It can be used as signal source in instruments and transmitters. It can be used as broad band noise sources which used to confuse enemy radar.
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Part – B 1. 2. 3. 4.
Explain the operation mechanism of two cavity Klystron amplifier with neat sketch. [N/D - 13] Explain the operation principle of the cavity klystron with neat sketch. [A/M - 13] Explain the bunching process of a two-cavity klystron and derive the expression for bunching parameter. [N/D - 13] Derive the equation of velocity modulated wave and discuss the concept of bunching effect. [N/D - 14] Two cavity klystron: The two-cavity klystron is a widely used microwave amplifier operated by the principles of velocity and current modulation. All electrons injected from the cathode arrive at the first cavity with uniform velocity. Those electrons passing the first cavity gap at zeros of the gap voltage (or signal voltage) pass through with unchanged velocity; those passing through the positive half cycles of the gap voltage undergo an increase in velocity; those passing through the negative swings of the gap voltage undergo a decrease in velocity. As a result of these actions, the electrons gradually bunch together as they travel down the drift space. The variation in electron velocity in the drift space is known as velocity modulation. The density of the electrons in the second cavity gap varies cyclically with time. The electron beam contains an ac component and is said to be current-modulated. The maximum bunching should occur approximately midway between the second cavity grids during its retarding phase; thus the kinetic energy is transferred from the electrons to the field of the second cavity. The electrons then emerge from the second cavity with reduced velocity and finally terminate at the collector. The charateristics of a two-cavity klystron amplifier are as follows: 1.Efficiency: about 40%. 2. Power output: average power ( CW power) is up to 500 kW and pulsed power is up to 30 MW at 10 GHz. 3. Power gain: about 30 dB. Reentrant Cavities The coaxial cavity is similar to a coaxial line shorted at two ends and joined at the center by a capacitor. The input impedance to each shorted coaxial line is given by
where e is the length of the coaxial line. Substitution of Eq. (9-2-l) in (9-2-2) results in
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The inductance of the cavity is given by
and the capacitance of the gap by
At resonance the inductive reactance of the two shorted coaxial lines in series is equal in magnitude to the capacitive reactance of the gap. That is, wL = 1/(wCg). Thus where v = 1/yr;;; is the phase velocity in any medium Velocity-Modulation Process When electrons are first accelerated by the high de voltage Vo before entering the buncher grids, their velocity is uniform:
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Fat im a im a Mic ha Mic el ha el
Col
Col
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In Eq. (9-2-10) it is assumed that electrons leave the cathode with zero velocity. When a microwave signal is applied to the input terminal, the gap voltage between the buncher grids appears as
Fat im a where V1 is the amplitude of the signal and V1 << Vo is assumed.
Mic ha el
In order to find the modulated velocity in the buncher cavity in terms of either the entering time to or the exiting time t1 and the gap transit angle 88 as shown in Fig. 9-2-2 it is necessary to determine the average microwave voltage in the buncher gap as indicated in Fig. 9-2-6. Since V1 << Vo , the average transit
Co
time through the buncher gap distance d is
leg
leg
leg
e
e
of En ine erin g
e
of Eng of ine Eng erin ine g erin g
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& Te ch no lo gy
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It can be seen that increasing the gap transit angle 08 decreases the coupling between the electron beam and the buncher cavity; that is, the velocity modulation of the beam for a given microwave signal is decreased. Immediately after velocity modulation, the exit velocity from the buncher gap is given by
DCE Bunching Process Once the electrons leave the buncher cavity, they drift with a velocity given by Eq. (9-2-19) or (9-2-20) along in the field-free space between the two cavities. The effect of velocity modulation produces bunching of the electron beam-or current modulation. The electrons that pass the buncher at Vs = 0 travel through with unchanged velocity vo and become the bunching center. Those electrons that pass the buncher cavity during the positive half cycles of the microwave input voltage Vs travel faster than the electrons that passed the gap when Vs = 0. Those electrons that pass the buncher cavity during the negative half cycles of the voltage Vs travel slower than the electrons that passed the gap when Vs = 0. At a distance of !:J..L along the beam from the buncher cavity, the beam electrons have drifted into dense clusters. Figure 9-2-8 shows the trajectories of minimum, zero, and maximum electron acceleration.
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The distance from the buncher grid to the location of dense electron bunching for the electron at tb is
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DCE
SCE
85
ECE
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5. Explain the working principle of reflex klystron and derive expression of bunching parameter [N/D - 13] 6. Explain the working principle of reflex klystron and derive expression for power and efficiency. [N/D – 15] REFLEX KLYSTRON If a fraction of the output power is fed back to the input cavity and if the loop gain has a magnitude of unity with a phase shift of multiple 27T, the klystron will oscillate. However, a two-cavity klystron oscillator is usually not constructed because, when the oscillation frequency is varied, the resonant frequency of each cavity and the feedback path phase shift must be readjusted for a positive feedback. The reflex klystron is a single-cavity klystron that overcomes the disadvantages of the twocavity klystron oscillator. It is a low-power generator of 10 to 500mW output at a frequency range of I to 25 GHz. The efficiency is about 20 to 30%. This type is widely used in the laboratory for microwave measurements and in microwave receivers as local oscillators in commercial, military, and airborne Doppler radars as well as missiles. The theory of the two-cavity klystron can be applied to the nalysis of the reflex klystron with slight modification. A schematic diagram of the reflex klystron is shown in Fig. The electron beam injected from the cathode is first velocity-modulated by the cavity-gap voltage. Some electrons accelerated by the accelerating field enter therepeller space with greater velocity than those with unchanged velocity. Some electrons decelerated by the retarding field enter the repeller region with less velocity. All electrons turned around by the repeller voltage then pass through the cavity gap in bunches that occur once per cycle. On their return journey the bunched electrons pass through the gap during the retarding phase of the alternating field and give up their kinetic energy to the electromagnetic energy of the field in the cavity. Oscillator output energy is then taken from the cavity. The electrons are finally collected by the walls of the cavity or other grounded metal parts of the tube. Figure 9-4-2 shows an Applegate diagram for the 1~ mode of a reflex klystron. Velocity Modulation
The analysis of a reflex klystron is similar to that of a two-cavity klystron. For simplicity, the effect of space-charge forces on the electron motion will again be neglected. The electron entering the cavity gap from the cathode at z = 0 and time to is assumed to have uniform velocity Visit : www.EasyEngineeering.net
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The same electron leaves the cavity gap at z = d at time ft with velocity
This expression is identical to Eq. (9-2-17), for the problems up to this point are identical to those of a two-cavity klystron amplifier. The same electron is forced back to the cavity z = d and time tz by the retarding electric field E, which is given by
This retarding field E is assumed to be constant in the z direction. The force equation for one electron in the repeller region is
where E = - VY is used in the z direction only, Yr is the magnitude of the repeller voltage, and I Yt sin wt I ~ (Yr + Yo) is assumed. Integration of Eq. (9-4-4) twice yields
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Fat im a im a Mic ha Mic el ha el
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Fat im a
DCE
Mic ha el
Col
Col
leg
Co t0 time for electron entering cavity gap at z = 0 t 1 time for same electron leaving cavity gap at z = d time for same electron returned by retarding field z = d and collected on walls of cavity
leg
leg
e
e
of En ine erin g
e
of Eng of ine Eng erin ine g erin g
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& Te ch no lo gy
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7. Draw cross sectional view of magnetron tube and explain how bunching occurs in it. Derive the expression for Hull cut-off voltage. [A/M - 12] 8. Explain any one practical applications of magnetron. [A/M - 12]. 9. Write a detailed note on cylindrical magnetron. [N/D - 13] 10. Explain the π mode of operation of magnetron. Mention few high frequency limitations [A/M - 15] MAGNETRON OSCILLATORS
Hull invented the magnetron in 1921 [1], but it was only an interesting laboratory device until about 1940. During World War II, an urgent need for high-power microwave generators for radar transmitters led to the rapid development of the magnetron to its present state. All magnetrons consist of some form of anode and cathode operated in a de magnetic field normal to of the crossed field between the cathode and anode, the electrons emitted from the cathode are influenced by the crossed field to move in curved paths. If the de magnetic field is strong enough, the electrons will not arrive in the anode but return instead to the cathode. Consequently, the anode current is cut off. Magnetrons can be classified into three types: 1. Split-anode magnetron: This type of magnetron uses a static negative resistance between two anode segments. 2. Cyclotron-frequency magnetrons: This type operates under the influence of synchronism between an alternating component of electric field and a periodic oscillation of electrons in a direction parallel to the field. 3. Traveling-wave magnetrons: This type depends on the interaction of electrons with a traveling electromagnetic field of linear velocity. They are customarily referred to simply as magnetrons.
Cylindrical Magnetron
A schematic diagram of a cylindrical magnetron oscillator is shown in Fig. 10-1-1. This type of magnetron is also called a conventional magnetron. In a cylindrical magnetron, several reentrant cavities are connected to the gaps. The de voltage Vo is applied between the cathode and the anode. The magnetic flux density Bo is in the positive z direction. When the de voltage and the magnetic flux are adjusted properly, the electrons will follow cycloidal pathsin the cathodeanode space under the combined force of both electric and magnetic fields as shown inFig.10-1-2. Equations of electron motion. The equations of motion for electrons in a cylindrical magnetron can be written with the aid of Eqs.(l-2-Sa) and (1-2-Sb) as
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DC
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DCE
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Since the slow-wave structure is closed on itself, or "reentrant," oscillations are possible only if the total phase shift around the structure is an integral multiple of 27T radians. Thus, if there are N reentrant cavities in the anode structure, the phase shift between two adjacent cavities can be expressed as
where n is an integer indicating the nth mode of oscillation. In order for oscillations to be produced in the structure, the anode de voltage must be adjusted so that the average rotational velocity of the electrons corresponds to the phase velocity of the field in the slow-wave structure. Magnetron oscillators are ordinarily operated in the 7T mode. That is
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Maxwell's equations subject to the boundary conditions. The solution for the fundamental cf> component of the electric field has the form [l]
where £ 1 is a constant and f3o is given in Eq. (10-1-18). Thus, the traveling field of the fundamental mode travels around the structure with angular velocity
where~ can be found from Eq. (10-1-19). When the cyclotron frequency of the electrons is equal to the angular frequency of the field, the interactions between the field and electron occurs and the energy is transferred. That is,
11. Explain the working principle of Travelling Wave Tube Amplifier [N/D - 15 ] Since Kompfner invented the helix traveling-wave tube (TWT) in 1944 [11], its basic circuit has changed little. For broadband applications, the helix TWTs are almost exclusively used, whereas for high-average- power purposes, such as radar transmitters, the coupled-cavity TWTs are commonly used. In previous sections klystrons and reflex klystrons were analyzed in some detail. Before starting to describe the TWT, it seems appropriate to compare the basic operating principles of both the TWT and the klystron. In the case of the TWT, the microwave circuit is nonresonant and the wave propagates with the same speed as the electrons in the beam. The initial effect on the beam is a small amount of velocity modulation caused by the weak electric fields associated with the traveling wave. Just as in the klystron, this velocity modulation later translates to current modulation, which then induces an RF current in the circuit, causing amplification. However, there are some major differences between the TWT and the klystron: The interaction of electron beam and RF field in the TWT is continuous over the entire length of the circuit, but the interaction in the klystron occurs only at the gaps of a few resonant cavities. The wave in the TWT is a propagating wave; the wave in the klystron is not. In the coupled-cavity TWT there is a coupling effect between the cavities, whereas each cavity in the klystron operates independently. As the operating frequency is increased, both the inductance and capacitance of the resonant circuit must be decreased in order to maintain resonance at the operating frequency. Because the gain-bandwidth product is limited
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by the resonant circuit, the ordinary resonator cannot generate a large output. Several nonresonant periodic circuits or slow-wave structures (see Fig. 9-5-2) are designed for producing large gain over a wide bandwidth.
DCE Slow-wave structures are special circuits that are used in microwave tubes to reduce the wave velocity in a certain direction so that the electron beam and the signal wave can interact. The phase velocity of a wave in ordinary waveguides is greater than the velocity of light in a vacuum. In the operation of traveling-wave and magnetron-type devices, the electron beam must keep in step with the microwave signal. Since the electron beam can be accelerated only to velocities that are about a fraction of the velocity of light, a slow-wave structure must be incorporated in the microwave devices so that the phase velocity of the microwave signal can keep pace with that of the electron beam for effective interactions. Several types of slow-wave structures are shown in figure
.
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Dhanalakshmi College of Engineering Department of ECE EC6701 – RF and Microwave Engineering Unit 5 – Microwave Measurements Part A 1. What is the principle by which high power measurements could be done by calorimetric method? [M/J – 08] Principle by calorimetric method are, Direct heating method Indirect heating method 2. State the demerits of single bridge power meter. [N/D – 08] The demerits of single bridge power meter are, The change of resistance due to a mismatch at the microwave input ports results in incorrect reading The themistor is sensitive to changes in the ambient temperature resulting in false reading 3. State any two sensors used to measure the power. Two sensors used to measure the power are, Barretter Thermistor
[N/D – 09]
4. What is bolometer? [M/J – 07] Bolometer is a power sensor whose resistance changes with temperature as it absorbs microwave power. Examples: Barretter, Thermistor. 5. What are the possible errors occur in measurement of standing wave ratio? The possible errors occur in measurement of standing wave ratio are, Vmax and Vmin may not be measured in the square law region of the crystal detector Probe thickness and depth may produce reflections in the line Residual VSWR arises due to mismatch impedance Harmonics and spurious signals from source cause measurement errors
[N/D – 12]
6. Define – SWR. [N/D – 13] In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transmission line. 7. Define − Return Loss [N/D – 07] The return loss is a measure of the power reflected by a line or network or device. Return loss (dB) = 10 log [input energy to the device / reflected energy at the input of the device] Return loss (dB) = 10 log [Pi/Pr] 8. What is the role of slow wave structure in TWT? [M/J – 13] The slow wave is a particular type of wave propagation, usually of the guided-wave type, and it is described mostly in the frequency-domain. Slow-wave structures are wave-guides or transmission lines in which the wave travels with a phase velocity equal to or less than a certain predesignated velocity of wave propagation. Visit : www.EasyEngineeering.net
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9. Distinguish between TWT and Klystron. TWT Interaction between EM field and beam of electrons in TWT is continuous over the entire length. In coupled cavity TWT, coupling effect takes place between cavities. TWT does not have resonant cavity. TWT has wider bandwidth of operation. TWT operates on lower efficiency.
[N/D – 13] Klystron Interaction in klystron occurs only at the gaps of resonant cavities. In klystron each cavity operates independently and there is no mutual coupling. Klystron has resonant cavities. Klystron has smaller bandwidth of operation. Klystron has comparatively high efficiency.
10. What is network analyzer? [N/D-16] The RF network analyser is used for characterising or measuring the response of devices at RF or even microwave frequencies. 11. Define − Reflection Loss Reflection loss is a measure of power loss during transmission due to the reflection of the signal as a result of impedance mismatch. 12. Define − Insertion Loss Insertion loss is a measure of loss of energy in transmission through a line or device compared to direct delivery of energy without the line or device. 13. What is a VSWR meter? VSWR meter is a highly sensitive, high gain, low noise voltage amplifier tuned normally at fixed frequency of 1 kHz at which microwave signals are modulated. This meter indicates calibrated VSWR reading for any loads. 14. What is calorimeter? Calorimeter is a convenient device for measuring the high power at microwave frequencies which involves conversion of microwave energy in to heat, absorbing the heat in a fluid and determine the temperature. 15. What are tunable detectors? The tunable detectors are used to demodulate the signal and couple the required output to high frequency scope analyzer. The low frequency demodulated output is detected using non reciprocal detector diode mounted in the microwave transmission line. 16. What is calorimetric direct heating method? In calorimetric direct heating method, the rate of production of heat can be measured by observing the rise in temperature of the dissipating medium. 17. What is calorimetric indirect heating method? In calorimetric indirect heating method, heat is transferred to another medium before measurement.
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Part B 1. Write notes on power measurement. [A/M - 12] 2. Describe the measurement of power at microwave frequencies in detail. [A/M - 14] 3. Describe how can the power of a microwave generator be measured using bolometer. [A/M - 15]
Power Measurement 1. Power is defined as the quantity of energy dissipated or stored per unit time. 2. Microwave power is divided into three categories – low power (less than 10mW), medium power (from 10mW to 10W) and high power (greater than 10w). 3. The general measurement technique for average power is to attach a properly calibrated sensor to the transmission line port at which the unknown power is to be measured. 4. The output from the sensor is connected to an appropriate power meter. The RF power to the sensor is turned off and the power meter zeroed. This operation is often referred to as “zero setting” or “zeroing.” Power is then turned on. 5. The sensor, reacting to the new input level, sends a signal to the power meter and the new meter reading is observed. 6. There are three popular devices for sensing and measuring average power at RF and microwave frequencies. Each of the methods uses a different kind of device to convert the RF power to a measurable DC or low frequency signal. The devices are the diode detector, the bolometer and the thermocouple. Diode Detector The low-barrier Schottky (LBS) diode technology which made it possible to construct diodes with metalsemiconductor junctions for microwave frequencies that was very rugged and consistent from diode to diode. These diodes, introduced as power sensors in 1974, were able to detect and measure power as low as −70 dBm (100 pW) at frequencies up to 18 GHz. Bolometer Sensor: Bolometers are power sensors that operate by changing resistance due to a change in temperature. The change in temperature results from converting RF or microwave energy into heat within the bolometric element. There are two principle types of bolometers, barretters and thermistors. A barretter is a thin wire that has a positive temperature coefficient of resistance. Thermistors are semiconductors with a negative temperature coefficient.
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Thermistor elements are mounted in either coaxial or waveguide structures so they are compatible with common transmission line systems used at microwave and RF frequencies. Power meters are constructed from balanced bridge circuits. The principal parts of the power meter are two self-balancing bridges, the meter-logic section, and the auto-zero circuit. The RF Bridge, which contains the detecting thermistor, is kept in balance by automatically varying the DC voltage Vrf, which drives that bridge. The compensating bridge, which contains the compensating thermistor, is kept in balance by automatically varying the DC voltage Vc, which drives that bridge. The power meter is initially zero-set (by pushing the zero-set button) with no applied RF power by making Vc equal to Vrfo (Vrfo means Vrf with zero RF power). After zero-setting, if ambient temperature variations change thermistor resistance, both bridge circuits respond by applying the same new voltage to maintain balance. If RF power is applied to the detecting thermistor, Vrf decreases so that
Where Prf is the RF power applied and R is the value of the thermistor resistance at balance. But from zero-setting, Vrfo= Vc so that
Which can be written
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Thermocouple Sensors Thermocouple sensors have been the detection technology of choice for sensing RF and microwave power since their introduction in 1974. The two main reasons for this evolution are: 1) they exhibit higher sensitivity than previous thermistor technology, and 2) they feature inherent square-law detection characteristic (input RF power is proportional to DC voltage out). Since thermocouples are heat-based sensors, they are true “averaging detectors.” Thermocouples are based on the fact that dissimilar metals generate a voltage due to temperature differences at a hot and a cold junction of the two metals. The power sensor contains two identical thermocouples on one chip, electrically connected as in Figure.
The thermocouples are connected in series as far as the DC voltmeter is concerned. For the RF input frequencies, the two thermocouples are in parallel, being driven through coupling capacitor Cc. Half the RF current flows through each thermocouple. Each thin-film resistor and the silicon in series with it have a total resistance of 100 Ω. The two thermocouples in parallel form a 50 Ω termination to the RF transmission line. The lower node of the left thermocouple is directly connected to ground and the lower node of the right thermocouple is at RF ground through bypass capacitor Cb. The DC voltages generated by the separate thermocouples add in series to form a higher DC output voltage. The principal advantage, however, of the two thermocouple scheme is that both leads to the voltmeter are at RF ground; there is no need for an RF choke in the upper lead. If a choke were needed it would limit the frequency range of the sensor. For a square wave modulated signal the peak power can be calculated from the average power measured as where T is the time period and Շis the pulse width.
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4. Write notes on measurement of impedance. [A/M - 12] 5. Explain the procedure for measuring impedance at microwave frequency with the aid of slotted line. [N/D - 13] 6. Explain the procedure for measuring impedance of load. [A/M - 14] 7. Describe how the frequency of a given microwave source can be measured. [A/M - 13] 5.7 MEASUREMENT OF WAVELENGTH AND IMPEADENCE
The impedance at any point on a transmission line can be written in the form R+jX For comparison SWR can be calculated
Where Reflection co-efficient
Z0= characteristics impedance of w/g at operating frequency Z= load impedance. The measurement is performed in following way. The unknown device is connected to the slotted line and the position of one minima is determined. The unknown device is replaced by movable short to the slotted line . Two successive minima positions are noted.The twice of the difference between minima position will be guidewave length. One of the minima
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is used as reference for impedance measurement .find the difference of reference minima and minima position obtained from unknown load. Let it be ‘d’. Take a smith chart , taking ‘1’ as centre, draw a circle of radius equal to S. mark a point on circumference of smith chart towards load side at a distance equal to d/g. join the centre with this point . find the point where it cut the drawn circle.the co-ordinates of this point will show the normalized impedance of load.
PROCEDURE: 1. Setup the components and equipments as shown in figure. 2. Setup variable attenuator at minimum attenuation position. 3. Keep the control knobs of VSWR meter as below: Range - 50db position 4. Input switch - Crystal low impedance Meter switch - Normal position Gain(Coarse & Fine)- Mid position 5. Keep the control knobs of Klystron power supply as below a. Beam voltage - ‘OFF’ Mod-switch -AM b. Beam Voltage knob-Fully anticlockwise c. Reflector Voltage- Fully clockwise d. AM- Amplitude knob- Around fully clockwise e. AM- Frequency knob – Around Mid position 6. Switch ‘ON’ the Klystron power supply, VSWR Meter and cooling fan switch. 7. Switch ‘ON’ the beam voltage switch and set beam voltage around 250V-300V with help of beam voltage knob. 8. Adjust the reflector voltage to get some deflection in VSWR meter. 9. Maximize the deflection with AM amplitude and frequency control knob of power supply. 10. Tune the plunger of Klystron Mount for maximum deflection. 11. Tune the reflector voltage knob for maximum deflection . 12. Tune the probe for maximum deflection in VSWR Meter. 13. Tune the frequency meter knob to get a ‘dip’ on the VSWR scale and note down the frequency directly from frequency meter. 14. Keep the depth of pin S S. Tuner to around 3-4 mm and lock it. 15. Move the probe along the slotted line to get maximum deflection. 16. Adjust VSWR meter gain control knob and variable attenuator until the meter indicates 1.0 on the normal db SWR scale. 17. Move the probe to next minimum position and note down the SWR S0 on the scale .also note down the probe position. Let it be ‘d’. 18. Remove the SS tuner and matched termination and place movable short at slotted line. The plunger of short should be at zero. Visit : www.EasyEngineeering.net
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19. Note the position of two successive minima position .let it be as d1 and d2 .Hence λg = 2(d1- d2). 20. Calculate
21. Find out the normalized impedance as described in the theory section. 22. Repeat the same experiment for other frequency if required.
8. Explain how low VSWR can be measured using a microwave bench. [N/D - 12] 9. Explain the measurement of high VSWR with the help of block diagram. [N/M - 13] 10. Explain the measurement of VSWR with neat block diagram. [N/D - 14]
MEASUREMENT OF SWR AND ATTUNUATION In a microwave network, if load impedance and line impedance are not matched, signal fed from the source is reflected again towards source causing standing wave pattern in the network. Voltage Standing Wave Ratio is a measure used for finding the magnitude of ration of reflected signals maximum and minimum amplitudes For analyzing standing wave pattern and to find S slotted line carriage is used in laboratory.
Low VSWR Measurements: (S<20)
Procedure: 1. Microwave Source is energized with 1 KHz square wave signal as carrier. 2. Tunable passive components are so adjusted to get reading across the VSWR meter in 30 dB scale. Visit : www.EasyEngineeering.net
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3. Detector (Tunable probe detector) is adjusted to get maximum power across the VSWR meter. 4. Slotted line carriage is moved from the load towards source to find the standing wave minimum position. 5. By adjusting the gain control knob of VSWR meter and attenuator the reading across the VSWR meter is made as 1 or 0 dB known as normalization. 6. Again the slotted carriage is moved towards source to find the next minimum position. The reading shown at this point in the VSWR meter is the ratio of magnitude of reflected signals minimum and maximum voltages ( ). min max VV S 7. VSWR meter has three different scales with different ranges as specified below. a. NORMAL SWR Scale 1 ---- 1 – 4 b. NORMAL SWR Scale 2 ---- 3.2 – 10 c. EXPANDED SWR Scale 3 ---- 1 – 1.33 8. If the device under test (DUT) is having the range of VSWR 1 – 4, reading is taken from the first scale from the top (NORMAL SWR Scale 1 – 1 – 4). 9. If the device under test (DUT) is having the range of VSWR 3.2 – 10, reading is taken from the second scale from the top (NORMAL SWR Scale 2 (3.2 – 10). 10. If the device under test (DUT) is having the range of VSWR 1 – 1.33, reading is taken from the third scale from the top (EXPANDED SWR Scale 3 (1 – 1.33). 11. If the device under test (DUT) is having the range of VSWR 10 – 40, a 20 dB range is selected in the VSWR meter and reading is taken from the first scale from the top (NORMAL SWR Scale 1 – 1 – 4) which is then multiplied by 10 for getting the actual reading. Possible Errors in Measurements: 1. Detector may not work square law region for both Vmax. and Vmin. 2. Depth of the probe in the slotted line carriage is made as minimum. If not, it may cause reflections in addition to the load reflections. 3. For the device having low VSWR, connector used for measurement must have proper matching with line impedance. 4. If the geometrical shape of the slotted line is not proper, Vmax. (or) Vmin. Value will not constant across the slotted line. 5. If the microwave signal is not properly modulated by a 1 KHz square wave, then signal becomes frequency modulated thereby it causes error in the Vmin. value measured. The value becomes lower than the actual. 6. Residual VSWR of slotted line carriage may cause error in the measurements. High VSWR Measurements - Double Minima Method - (S>20)
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Measurement of high VSWR needs separate procedure because the detector may not be tuned to work in square law region. An alternate method known as double minimum method is used for finding high VSWR with the same experimental set up as shown above. Procedure: 1. Microwave Source is energized with 1 KHz square wave signal as carrier. 2. Tunable passive components are so adjusted to get reading across the VSWR meter in 30 dB scale. 3. Detector (Tunable probe detector) is adjusted to get maximum power across the VSWR meter. 4. Slotted line carriage is moved from the load towards source to find the standing wave minimum position. Let it be d1. 5. Slotted line carriage is moved further to find the next immediate minimum position. Let it be d2. Now g = 2 (d1 - d2) 6. By adjusting the gain control knob of VSWR meter and attenuator the reading across the VSWR meter is made as 3 dB at this minimum position. 7. By taking this point as reference, slotted line carriage is moved on either side. The points at which the VSWR meter shows 0 dB reading on both sides are noted as x1 and x2. 8. High VSWR can be calculated by using the formula VSWR Measurements by Return Loss (Reflectometer) Method: To overcome the difficulties faced in slotted line carriage for measuring VSWR, reflectometer can be used. Reflectometer is a device having two directional couplers combined together with ideal coupling factor and directivity. It is a four-port device. Experimental Procedure: 1. Microwave Source is energized with 1 KHz square wave signal as carrier. 2. Tunable passive components are so adjusted to get reading across the VSWR meter in 30 dB scale. 3. Detector (Tunable probe detector) is adjusted to get maximum power across the VSWR meter. 4. Port 2 is with a movable short and is adjusted for getting the output across the detector to unity in VSWR meter. Port 3 is matched terminated. 5. VSWR meter and matched load at port4 and port 3 are interchanged. The output of the port3 is noted which should be ideally equal to the output from port 4. 6. Without disturbing the VSWR meter adjustment, the unknown load is connected at port 2 by replacing the short and the output at port3 is noted to obtain
directly from the VSWR meter. Return loss =
This method is well suited for loads having low VSWR. The major sources of errors are
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1. Unstability of the signal source causes a change of signal power level during measurement of input and reflected signals. 2. Non-ideal directional couplers and detectors are also sources of error.
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5.9 Q AND PHASE SHIFT Microwave frequency can be measured by a number of different mechanical and electronic techniques. 1. Mechanical techniques 2. Slotted Line Method (Indirect Method) The standing waves setup in a transmission line or a waveguide produce minima every half wavelength apart.
These minima are detected and the distance between them is measured. From which the wavelength and frequency can be calculated by
Resonant Cavity Method (Direct Method) The most commonly used type of microwave frequency meter is wave meters. It consists of a cylindrical or coaxial resonant cavity. The size of the cavity can be altered by adjustable plunger. The cavity is
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designed in such a way that for a given position of the plunger, the cavity is resonant only at one frequency in the specified range.
The cavity is coupled to the waveguide through an iris in the narrow wall of the waveguide. If the frequency of the wave passing through the waveguide is different from the resonance frequency of the cavity, the transmission is not affected. If these two frequencies coincide then the wave passing through the waveguide is attenuated due to power loss. It will be indicated as a dip in the meter. Electronic Technique Counter Method An accurate measurement of microwave frequency can be measured here. The input signal is divided into two equal signals by a resistive power divider. These two parts of the signal are fed to 2 mixers. The mixer 1 is used in the input PLL (Phase Locked Loop) and the mixer 2 is used to determine the harmonic number. The frequency f1 of the input PLL is also fed to the direct counter circuits. The input PLL consists of a voltage controlled oscillator (VCO), mixer, an IF amplifier, a phase detector and a gain control block. The VCO searches over its range until an IF signal equal to 20MHz is found. Phase lock occurs when the phase detector output sets the VCO frequency f1 such that
where IF1 = 20 MHz at the phase lock and fx is the unknown frequency to be measured.
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The f1 is translated to a frequency f2 so that
where f0 = 20 MHz offset frequency. This is done by a frequency translation unit (FTU). The frequency f2 drives the second sampler and produces a second output. IF2 is given as
By mixing IF2 with IF1 and rejecting 20 MHz and higher frequencies, nf0 is obtained. Counting the number of zero crossing for the period of f0, determines the harmonic number n of the phase lock loop. The input frequency is then calculated by presetting into IFref counter, measuring f1 and extending gate time according to number n.
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