A Laboratory Report On
Wireless Communication Hardware Design and Simulation: Part II Design Project: Coupler and Wilkinson Power Divider Design Submitted by: Amit Prakash Singh and Abhinay Dubey Integrated Dual Degree, IV year Department of Electronics & Communication Engineering Indian Institute of Technology Roorkee Submitted to: Dr. N.P. Pathak, Assistant Professor, Department of Electronics & Communication Engineering Indian Institute of Technology Roorkee
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Wireless Communication Hardware Design and Simulation: Part II
Acknowledgements We are very thankful to Dr. N.P. Pathak for providing us constant encouragement and support during the course of the Wireless Communications Lab. Without his help it would not have possible to complete this report. We are also highly indebted to Mr. Raja Ram, the laboratory assistant, for helping us in the lab. Amit Prakash Singh Abhinay Dubey Integrated Dual Degree IV year Indian Institute of Technology Roorkee
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Wireless Communication Hardware Design and Simulation: Part II
Contents Directional Couplers ...................................................................................................................................... 4 Definitions ................................................................................................................................................. 5 Forward versus backward wave couplers ................................................................................................. 5 Hybrid (3 dB) couplers .............................................................................................................................. 5 180 degree hybrid couplers .................................................................................................................. 6 90 degree hybrid couplers .................................................................................................................... 7 Single‐box branchline couplers ................................................................................................................. 9 Rat‐race couplers .................................................................................................................................... 12 Wilkinson Power Divider ......................................................................................................................... 15 Two‐port Wilkinsons ........................................................................................................................... 15 Coupler Design in Microstrip ...................................................................................................................... 17 Specification: Design a 3‐dB, 90 Branch Line Coupler at 2.5Ghz ............................................................ 17 Specification: Design 15‐dB Single Section Parallel Coupled Backward Wave Coupler at 2.4 Ghz ........ 20 Specification: To Design a 3‐dB Rat‐Race Coupler at 2.4GHz ................................................................. 22 Microstrip Wilkinson Power Divider Design ............................................................................................... 24 Specification: To Design a 3‐dB Wilkinson Power Divider at 2.4GHz ...................................................... 24
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Wireless Communication Hardware Design and Simulation: Part II
Power splitters and couplers are passive microwave components used for distributing or combining microwave signals. A splitter can be used as either a power combiner or a power divider, it is a reciprocal device.
Directional Couplers Directional couplers are four-port circuits where one port is isolated from the input port. Directional couplers are passive reciprocal networks, which you can read more about on our page on basic network theory. All four ports are (ideally) matched, and the circuit is (ideally) lossless. Directional couplers can be realized in microstrip, stripline, coax and waveguide. They are used for sampling a signal, sometimes both the incident and reflected waves (this application is called a reflectometer, which is an important part of a network analyzer). Directional couplers generally use distributed properties of microwave circuits, the coupling feature is generally a quarter (or multiple) quarter wavelengths. Lumped element couplers can be constructed but without distributed properties are non-directional. What do we mean by "directional"? A directional coupler has four ports, where one is regarded as the input, one is regarded as the "through" port (where most of the incident signal exits), one is regarded as the coupled port (where a fixed fraction of the input signal appears, usually expressed in dB), and an isolated port, which is usually terminated. If the signal is reversed so that it enter the "though" port, most of it exits the "input" port, but the coupled port is now the port that was previously regarded as the "isolated port". The coupled port is a function of which port is the incident port. Looking at the generic directional coupler schematic below, if port 1 is the incident port, port 2 is the transmitted port (because it is connected with a straight line). Either port 3 or port 4 is the coupled port, and the other is the isolated port, depending on whether the coupling mode is forward or backward.
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Wireless Communication Hardware Design and Simulation: Part II
Definitions Let port 1 be the input port, port 2 be the "through" port. For a backward wave coupler, port 4 is the coupled port and port 3 is the isolated port. Ideally, power into port 1 will only appear at ports 2 and 4, with no power at port 3, but in real couplers some power leaks to port 3. For an incident signal at port 1 of power P1 (and output powers P2, P3 and P4 at ports 2, 3 and 4), then: Insertion Loss (IL) = 10 log
20log 20
Coupling Factor (CF) = 10 Isolation (I) = 10
20
Directivity (D) = 10
31
20
Note that these numbers are positive in dB. Note that directivity requires two, two-port S-parameter measurements; the other quantities require only one. Directivity is the ratio of isolation to coupling factor. In decibels, isolation is equal to coupling factor plus directivity.
Forward versus backward wave couplers Waveguide couplers couple in the forward direction (forward-wave couplers); a signal incident on port 1 will couple to port 3 (port 4 is isolated). Microstrip or stripline couplers are "backward wave" couplers. In the schematic above, which means for a signal incident on port 1, port 4 is the coupled port (port 3 is isolated). The coupled port on a microstrip or stripline directional coupler is closest to the input port because it is a backward wave coupler. On a waveguide broadwall directional coupler, the coupled port is closest to the output port because it is a forward wave coupler.
Hybrid (3 dB) couplers Hybrid couplers are the special case of a four-port directional coupler that is designed for a 3-dB (equal) power split. Hybrids come in two types, 90 degree or quadrature hybrids, and 180 degree hybrids.
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Wireless Communication Hardware Design and Simulation: Part II
180 degree hybrid couplers These include rat-race couplers and waveguide magic tees. Here we will look at the rat-race and introduce the vector and shorthand notation that is often used when referring to 180 degree hybrid couplers.
Here's a plot that shows the ideal, "classic" rat-race response (equal split at center frequency).
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Wireless Communication Hardware Design and Simulation: Part II
The rat-race gives about 32% bandwidth for a phase error of +/-10 degrees from the ideal 180 degree split.
90 degree hybrid couplers These are often called quadrature couplers, and include Lange couplers, the branchline coupler, overlay couplers, edge couplers, and short-slot hybrid couplers. Here we will just look at a branchline, and show you some of the "short hand" notation that is often used when referring to hybrids. A quadrature coupler is one in which the input is split into two signals (usually with a goal of equal magnitudes) that are 90 degrees apart in phase. Types of quadrature couplers include branchline couplers (also known as quadrature hybrid couplers), Lange couplers and overlay couplers. Below the branchline is used as a combiner. The input signals are vectors of magnitude A and B, then the outputs are as shown. Note that because we are dealing with voltages, the outputs have a square-root-of-two factor. Power is split exactly in half (-3 dB), equal to the square of the voltages.
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Wireless Communication Hardware Design and Simulation: Part II
Now let's look at it as a divider. Here only an input signal is present at port A. It splits by 3 dB at the two outputs, and is isolated from Port B (ideally zero energy comes out this port).
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Wireless Communication Hardware Design and Simulation: Part II
Now let's look at the response of this component, and compare it to the "classic" rat-race:
The bandwidth is less. If we just look at the frequency where the 180 degree split is within +/- 10 degrees, it is about 20% (0.9 to 1.1 GHz). Referring to the classic rat-race above, it has 32 percent bandwidth for the same phase error.
Singlebox branchline couplers The branchline the simplest type of quadrature coupler, since the circuitry is entirely planar. A ideal single-box branchline coupler is shown below. Each transmission line is a quarter wavelength. However, 3/4, 5/4 or 7/4 wavelengths (etc.) could also be used on each arm if the circuit layout requires it, the penalty is paid in decreasing bandwidth. A signal entering the top left port (port 1 in the figure) is split into two quadrature signals on the right (ports 2 and 3), with the remaining port 4 fully isolated from the input port at the center frequency. Remember that the lower output port (port 3) has the most negative transmission phase since it has the farthest path to travel.
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Wireless Communication Hardware Design and Simulation: Part II
Ideal branchline coupler The next figure shows the response of an ideal branchline coupler where the each side is a quarter wavelength at 10,000 MHz (10 GHz). The first graph shows the losses from the input to the two output arms. S21 is the transmission loss from the top port to the upper right port, S31 is from the input to the lower right port. Using the ideal transmission line impedances shown above provides a equal 3 dB split at the center frequency. The markers have been aligned to show the 1-dB bandwidth of the coupler, which is 2580 MHz or 25.8%.
Power split of ideal branchline coupler The second graph shows that the bandwidth where the device has better than 14 dB return loss (1.5:1 VSWR) is 2080 MHz, or 20.8%. The isolation (power coupled to the terminated port) is also plotted here and is very nearly equal to the return loss.
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Wireless Communication Hardware Design and Simulation: Part II
Return loss (blue) and isolation (red) of ideal branchline coupler The next plot shows the phase difference between the two outputs (ideally 90 degrees, remember?) For +/-10 degrees the bandwidth is about 4300 MHz, or 43%.
Phase response of ideal branchline coupler
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Wireless Communication Hardware Design and Simulation: Part II
Ratrace couplers Applications of rat-race couplers are numerous, and include mixers and phase shifters. The ratrace gets its name from its circular shape, shown below. The circumference is 1.5 wavelengths. For an equal-split rat-race coupler, the impedance of the entire ring is fixed at 1.41xZ0, or 70.7 ohms for a 50 ohm system. For an input signal Vin, the outputs at ports 2 and 4 are equal in magnitude, but 180 degrees out of phase.
Rat-race coupler (equal power split) The coupling of the two arms is shown in the figure below, for an ideal rat-race coupler centered at 10 GHz (10,000 MHz). An equal power split of 3 dB occurs at only the center frequency. The 1-dB bandwidth of the coupled port (S41) is shown by the markers to be 3760 MHz, or 37.6 percent.
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Wireless Communication Hardware Design and Simulation: Part II
Power split of ideal rat-race coupler The graph below illustrates the impedance match of the same ideal rat-race coupler, at ports 1 and 4. By symmetry, the impedance match at port 3 is the same as at port 1 (S11=S33). For better than 2.0:1 VSWR (14 dB return loss), a bandwidth of 4280 MHz (42.8%) is obtained.
Impedance match of ideal rat-race coupler The next graph shows the isolation between port 1 and port 3 (S31). In the ideal case, it is infinite at the center frequency. The bandwidth over which greater than 20 dB isolation is obtained is 3140 MHz, or 31.4%.
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Wireless Communication Hardware Design and Simulation: Part II
Isolation of ideal rat-race coupler Below the phase difference between arms 2 and 4 is plotted. At the center frequency. a perfect 180 degree difference is observed. The bandwidth that better than +/- 10 degrees is maintained is 3200 MHz, or 32%.
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Wireless Communication Hardware Design and Simulation: Part II
Wilkinson Power Divider The Wilkinson power splitter was invented around 1960 by an engineer named Ernest Wilkinson. It splits an input signal into two equal phase output signals, or combines two equalphase signal into one in the opposite direction. Wilkinson relied on quarter-wave transformers to match the split ports to the common port. Because a lossless reciprocal three-port network cannot have all ports simultaneously matched, Wilkinson knew he had to cheat so he added one resistor and the rest is history. The resistor does a lot more than allow all three ports to be matched, it fully isolates port 2 from port 3 at the center frequency. Amazingly, the resistor adds no resistive loss to the power split, so an ideal Wilkinson splitter is 100% efficient.
Twoport Wilkinsons In its simplest form, an equal-amplitude, two-way split, single-stage Wilkinson is shown the figure below. The arms are quarter-wave transformers of impedance 1.414xZ0 (thanks for the correction, Rod!) Here we show a three-port circuit (the most common in practice by far, but Wilkinson described an N-way divider).
Ideal two-port Wilkinson splitter
S-parameters of ideal 2-way Wilkinson power splitter Here is how the Wilkinson splitter works as a power divider: when a signal enters port 1, it splits into equal-amplitude, equal-phase output signals at ports 2 and 3. Since each end of the isolation
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Wireless Communication Hardware Design and Simulation: Part II
resistor between ports 2 and 3 is at the same potential, no current flows through it and therefore the resistor is decoupled from the input. The two output port terminations will add in parallel at the input, so they must be transformed to 2xZ0 each at the input port to combine to Z0. The quarter-wave transformers in each leg accomplish this; without the quarter-wave transformers, the combined impedance of the two outputs at port 1 would be Z0/2. The characteristic impedance of the quarter-wave lines must be equal to 1.414xZ0 so that the input is matched when ports 2 and 3 are terminated in Z0. Okay, what about as a power combiner? Consider a signal input at port 2. In this case, it splits equally between port 1 and the resistor R with none appearing at port 3. The resistor thus serves the important function of decoupling ports 2 and 3. Note that for a signal input at either port 2 or 3, half the power is dissipated in the resistor and half is delivered to port 1. Why is port 2 isolated from port 3 and vice-versa? Consider that the signal splits when it enters port 2. Part of it goes clockwise through the resistor and part goes counterclockwise through the upper arm, then splits at the input port, then continues counterclockwise through the lower arm toward port 3. The recombining signals at port 3 end up equal in amplitude (half power or the CW signal is lost in resistor R1, while half of the CCW signal is output port 1. And they are 180 degrees out of phase due to the half-wavelength that the CCW signal travels that the CW signal doesn't. The two signal voltages subtract to zero at port 3 and the signal disappears, at least under ideal circumstances. In real couplers, there is a finite phase through the resistor that will limit the isolation of the output ports.
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Wireless Communication Hardware Design and Simulation: Part II
Coupler Design in Microstrip In this laboratory we designed three couplers, namely, Branch Line Coupler, Backward Wave Coupler and Rat Race Coupler. All designs were done using Transmission line Calculator tool of Serenade ™ . Once the design was completed on paper, the Coupler was designed in Ansoft Designer ™ with Planar EM design. Then a simulation was run and the S parameters obtained in the Simulation along with the simulated design have been shown.
Specification: Design a 3dB, 90 Branch Line Coupler at 2.5Ghz DESIGN: From the given specification, Since the coupling is given as 3‐dB Therefore, we can write: 20
|
|
|
|
|
20 |
1
|
√2
|
3
√2 √2 √2 Or √2
√2 Or
Since Z0 =50Ω, we get impedance of the series and shunt branches as: 50 √2
35.4Ω 50Ω
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Wireless Communication Hardware Design and Simulation: Part II
To get MIC layout, we need width and length of transmission line. CALCULATION RESULTS Z0=50 Ω W= 3.611mm l=19.4456mm Keff=2.5826
Z=35.4 Ω W=6.00mm L=19.036mm Keff=2.6949
SIMULATION RESULTS
Branch Line Coupler S Parameters
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Wireless Communication Hardware Design and Simulation: Part II
Coupler Layout
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Wireless Communication Hardware Design and Simulation: Part II
Specification: Design 15dB Single Section Parallel Coupled Backward Wave Coupler at 2.4 Ghz DESIGN From the given Specifications Mid band operating frequency, f0= 2.4 Ghz Port Impedance, Z0= 50Ω Mean Coupling, C0=15dB Coupling Length,
5
15
15
20 10
0.1778
1 1
59.8435Ω
1 1
41.7756Ω
Dimension required for the fabrication of coupler in Microstrip configuration is given below CALCULATION RESULTS W=3.411mm S=0.862mm L=19.63mm
59.8435 Ω Keff=2.7411
41.8 Ω Keff=2.3252
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Wireless Communication Hardware Design and Simulation: Part II
SIMULATION RESULTS: S Parameters and Layout
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Wireless Communication Hardware Design and Simulation: Part II
Specification: To Design a 3dB RatRace Coupler at 2.4GHz DESIGN Rat‐race circuit is shown in the fig. Output signals from ports 2 and 4 doffer in phase by 1800(In Contrast in BLC where the phase difference is 90o). An interesting and important design feature arises by considering the quarter wave transformer action of this coupler. Only ports 2 and 4 exibit this action because port 3 is half‐wave separated from the input feeding port 1. Thus, the net effective load on the inner ring lines feeding ports 2 and 4 amounts to 2Z0 (two Z0 loads appearing, equivalently, in series). Now, the characteristic impedance Z0 of any transforming line between two impedances Z01 and Z02 is known to equal
. In this case, the two impedances are
and 2
respectively, so the
impedance of the intervening line (i.e. the ring) must be: 2
Or √2 Thus the characteristic impedance of the line forming the ring itself must be √2 times that of the feeder line impedances. When the impedances of all the feeder lines is 50Ω, the ring characteristic impedance is 70.7Ω. CALCULATION RESULTS =50Ω W=3.611mm Keff=2.5826
√2=70.7Ω W=1.99mm Keff=2.4698 Λg=79.562mm
SIMULATION RESULTS: S Parameters and Layout
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Wireless Communication Hardware Design and Simulation: Part II
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Wireless Communication Hardware Design and Simulation: Part II
Microstrip Wilkinson Power Divider Design In this laboratory we designed a Wilkinson Power Divider. The design was done using Transmission line Calculator tool of Serenade ™ . Once the design was completed on paper, the Power Divider was designed in Ansoft Designer ™ with Planar EM design. Then a simulation was run and the S parameters obtained in the Simulation along with the simulated design have been shown.
Specification: To Design a 3dB Wilkinson Power Divider at 2.4GHz DESIGN The Wilkinson Power Divider is a 3‐Port network which has the useful property of being lossless when the output ports are matched; i.e. only reflected power is dissipated. The S‐Matrix of a power divider satisfying the following requirements 1. Matched Input and Output Ports 2. Equal power division 3. Isolation between Output ports will be given by:
√2
0 1 1
1 0 0
1 0 0
Port 1 is taken to be the input and ports 2 and 3 are the two outputs. It may be noticed that this matrix will not be unitary (whatever phases one takes), and hence cannot be built using purely lossless passive structure such as transmission lines, inductors, capacitors only. The Wilkinson Power divider incorporates a lumped resistor to give the desired matrix. The layout of the Wilkinson Power divider is shown in fig below. Zd is the terminating impedance in all 3 ports
WILKINSON POWER DIVIDER For a 50Ω system,
=50 Ω, Dimensions are given in the following table:
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Wireless Communication Hardware Design and Simulation: Part II
CALCULATION RESULTS =50Ω W=3.611mm Keff=2.5826
√2 =70.7Ω W=1.99mm Keff=2.4863 L(90o)=19.891mm
SIMULATION RESULTS: S Parameters and Layout
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Wireless Communication Hardware Design and Simulation: Part II