ElecEng 4/6FJ4 LABORATORY MODULE #4 Introduction to Scattering Parameters and Vector Network Analyzers: Measurements of 1- Port Devices I. Objectives The purpose of this module is to help the students get a deeper understanding of the physical meaning of the scattering parameters (or S-parameters), the network parameters used to characterize the microwave circuits and devices. The students will also gain hands-on experience in using vector network analyzers (VNAs) to measure the S-parameters of 1-port microwave components. The VNA is an essential instrument in the microwave lab and in the telecommunications industry. Its operation is a core subject of microwave engineering courses. The lectures of ElecEng 4FJ4 do cover the general topic of microwave networks and their characterization in terms of S-parameters. The lectures also treat in depth the operation of the VNAs and their calibration. Thus, this laboratory module supports the lectures in both its content and hands-on experience. On the other hand, this laboratory module is stand-alone, i.e., it can be performed independently from the lectures. All the necessary knowledge to perform the exercises is provided in the DISCUSSION part. The students must prepare for the 3-hour laboratory beforehand by reading the DISCUSION part. If the students come to the lab unprepared, it is likely that they will not be able to complete the exercises on time. II. Preparing the Lab Report The student is expected to bring along a printout of this guide. The Lab Report will have to be prepared after the end of the lab exercise. This is because the measured results will have to be exported to files, plotted and attached to the Lab Report. The Lab Report consists of: (1) the title page, (2) the PROCEDURE part, (3) the REVIEW QUESTIONS, and (4) the ATTACHMENTS (plots of results). The student is expected to hand in the lab report to the teaching assistant (TA) no later than ONE WEEK after the completion of the module. Handing in an electronic copy of the Lab Report via email is admissible but is subject to arrangement with the TA. PLEASE WRITE DOWN YOUR NAME AND STUDENT ID ON THE TITLE PAGE! III. Grading the Lab Report Total points: 100 Penalty for a missing item in the PROCEDURE part: 5 points Penalty for a missing plot or table in the PROCEDURE part: 10 points Penalty for a missing or wrong answer in the REVIEW QUESTIONS part: 10 points IV. Feedback We value your opinion. Direct your recommendations, opinions, and criticism to the Instructor (Prof. Nikolova) at nikolova@ieee.org.
1 ElecEng 4/6FJ4 LABORATORY MODULE #4 INTRODUCTION TO NETWORK SCATTERING PARAMETERS AND VECTOR NETWORK ANALYZERS (VNAs) Student Name: Student ID: Student Signature: Date: TA Name: TA Signature: Date: REPORT GRADE: (provided no later than one week after the report submission)
EE4/6FJ4 LABORATORY: INTRODUCTION TO NETWORK SCATTERING PARAMETERS AND VECTOR NETWORK ANALYZERS (VNAs) 2 GENERAL NOTES ON HANDLING THE INSTRUMENT The Vector Network Analyzer (VNA) is an essential tool in characterizing radio-frequency (RF), microwave and millimeter-wave devices and networks. It is a sophisticated instrument combining sensitive radio circuitry with digital electronics and a computer. The VNA is very expensive. Please handle with care! Follow the instructions of the TA carefully. Do not push buttons randomly. If in doubt, call the TA for assistance. Do not bend the cables excessively. Connect the measured devices to the cable connectors carefully. Be gentle on the connectors they are easy to destroy. Do not twist the device while screwing the cable to it. Tighten as much as your fingers can go without excessive effort; then use the special wrench. Once finished with a device, please put it back in its box. When finished with the lab procedures below, call the TA who will make sure that all connectors, cables, and devices are in place and are properly stored. You can then leave.
I. DISCUSSION 1. Power Waves and the Scattering Parameters Electrical engineers are familiar with the various parameters used to characterize an N-port (2Nterminal) network such as the Z-parameters (the impedance matrix), the Y-parameters (the admittance matrix), the H-parameters (the hybrid matrix), the ABCD parameters of 2-ports (the transmission matrix) and others. All of these parameter sets relate the voltages and the currents at the networks ports. Figure 1 shows the common symbols for a single-port, a 2-port and a 3-port network with the convention for the directions of the port voltages and currents. Knowing the network parameters of a circuit or a device allows for treating it as a black box (i.e., we do not need to know what is inside) and for incorporating it in the analysis of a larger network which it is part of. As seen from Figure 1, every port is a pair of terminals (a pair of wires) where the module interconnects with other modules in a more complex network. A. Power Waves The problem arising in microwave-network analysis is that their interconnects are not simple two-terminal wires. Their interconnects are generally referred to as waveguides (the name is selfexplanatory). Strictly speaking, all transmission lines are waveguides, as long as they are electrically long. The waveguides can take the form of coaxial cables, printed traces in an integrated circuit (IC), metallic waveguides or dielectric (optical) fibers. While in the first two cases (a coaxial cable or a pair of printed traces) we still could define and measure voltages and currents (if the frequency is sufficiently low), this is impossible in the case of metallic waveguides and optical fibers. Thus, all network parameters based on the current/voltage port variables are inadequate in such cases. Moreover, even if we could define and measure voltages and currents for certain waveguides, we still would face a significant inconvenience, namely, the electrical length from the port crosssection (or, equivalently, from the device connectors) to the actual high-frequency structure enclosed by the module. Adjusting this length often necessary in the design of the device would change the voltage and current port quantities in a fairly complicated manner as these represent the superposition of incident and reflected voltage and current waves along the interconnect. As a result, the network parameters would change in a very complicated way as functions of these internal transmission lines. For the above two reasons, microwave engineers prefer to work with wave quantities directly, the port incident and reflected waves. By convention, the incident port waves are denoted by the symbol a while the reflected port waves are denoted by b. Figure 2 illustrates the conventions in describing 1-port, 2-port and 3-port microwave networks in terms of the wave quantities. The wave quantities are in essence traveling waves where the incident waves travel toward the device while the reflected waves travel away from the device. The incident waves are also called incoming while the reflected waves are also called outgoing or scattered. In fact, the terms outgoing or scattered is often preferred because a wave traveling away from the device may not be due to reflection at the port but it may be due to transmission through the device. 3 V 1 I 1 V 1 I 1 I2 V1 V2 V3 I1 I2 I3 V 2 (a) (b) (c) Figure 1: Examples of electrical networks and their symbol definitions: (a) 1-port, (b) 2-port, and (c) 3-port.
4 a 2 b 2 S 32 S 33 b 3 a 3 S 22 S 23 a 1 Γ=S11 b1 S a 21 1 S11 S b 22 1 S 12 b a 2 2 S 21 S12 S31 S 13 S 11 a1 b 1 (a) (b) (c) Figure 2: Examples of microwave networks and their symbol definitions: (a) 1-port device with incident and reflected waves and its reflection coefficient Γ, which is identical to the only element of its scattering matrix ( S 11 ); (b) 2-port device with its four wave quantities and four scattering parameters, and (c) 3-port device with its six wave quantities and nine scattering parameters. The physical meaning of the incident and reflected port waves is easy to understand. Any given port, say the n-th port, of a microwave device, is connected to its respective (n-th) waveguide (or a transmission line). Assume first that a microwave generator is connected at the other end of this n-th waveguide. It will generate a wave traveling toward the device. Provided this waveguide is loaded with a matched impedance (for example, our device presents a matched load to the waveguide), there will be no reflected wave, and the waveguide will carry exactly the incident wave a n toward the device. The outgoing wave b n can be understood in a similar manner. Assume that microwave power is fed into the device through another port, say the m-th port, where m n. Then we can expect that, in general, some power will emerge at the n-th port and will travel down the n-th waveguide away from the device. Now assume that this waveguide is infinitely long or is loaded with a matched load at the other end. Then that outgoing traveling wave is the only wave carried by the waveguide. This is exactly the wave b n. The wave quantities are complex numbers. The wave-quantity magnitude is the square root of the power carried by the traveling wave. Thus, if we denote the power carried by the incoming wave at the n-th port by P n + and that carried by the outgoing wave by Pn, we have an = P n +, bn = Pn 1/2 (W ). (1) This is why the wave quantities are also referred to as root-power waves (or simply power waves). The angles (or the phases) of the wave quantities correspond to the phases of the respective traveling waves, which, in electromagnetic terms, are the phases of their electric fields at the port: an = E n +, bn = En. (2) There is a straightforward relationship between the power waves and the voltage and current waves that exist in TEM transmission lines such as the coaxial cable or the twin-lead line, which electrical engineers are familiar with. If the transmission line at the n-th port has real characteristic impedance Z 0n (loss-free line), which is normally the case in measurements, the incident and the outgoing root-power waves a n and b n relate to the (RMS) phasors of the incident voltage wave V n + and the reflected voltage wave Vn, respectively, as
+ n V Vn 1/2 an =, bn = (W ). (3) Z0n Z0n It can be shown that in the general case of a complex characteristic impedance, the denominators in the expressions in (3) should be Re Z 0 ( Re Z 0n > 0 ). B. Scattering Parameters n The scattering matrix (or S-matrix) relates the vector of incident waves a to the vector of scattered waves b as b = Sa (4) where a = [ aa 1 2 a ] T N, b = [ bb 1 2 b ] T N, and S11 S1N S =. (5) SN 1 SNN The elements of the scattering matrix S are referred to as the scattering parameters (or S- parameters). They are in essence the reflection and transmission coefficients of the microwave device. The diagonal elements of S are the reflection coefficients. As follows from (4), the reflection coefficient at the i-th port S ii ( i = 1,, N ) can be written in terms of the incoming and outgoing power waves at the i-th port as: bi S =, k i. (6) ii a i ak = 0 The off-diagonal elements of S are the transmission coefficients. Similarly to (6), the transmission coefficient from the i-th port to the j-th port S ji is expressed in terms of the outgoing wave b j at the j-th port and the incoming wave at the i-th port a i as: bj S =, k i. (7) ji a i ak = 0 Notice the condition a k = 0, k i, in (6) and (7). It tells us that in order to measure S ji or S ii, the excitation must be provided at the i-th port (so that ai 0 ) while at all other ports incident waves must not be present. This imposes two requirements on these ports: (1) they must not be connected to generators, and (2) they must be loaded with a matched impedance so that the power waves leaving the device through them do not get reflected back toward the device. The S-parameters are complex numbers. The magnitude of the S ji parameter shows the proportion of the root-power (or the signal) incident on port i, which reaches port j and leaves the device. If i = j, the same principle applies S ii shows the proportion of the signal incident on port i, which, as a result of the interaction with the device, is injected back into the i-th port and travels away as a reflected wave toward the generator. For example, a load consisting of a shorted loss-free transmission line (a 1-port network) is characterized by an S-parameter of unity magnitude, i.e., S 11 = 1, indicating full reflection of the incident power back to the generator. However, if the transmission line is loaded with a matched load, the reflection is zero and S 11 = 0. In another example, a loss-free transmission line (a 2- port network) has transmission coefficients of unity magnitude, i.e., S21 = S21 = 1, indicating that all of the incident power on one of the ports is transmitted through the other port, provided that this other port is matched remember the condition a k = 0, k i! The phase of the S parameter shows the change in the wave s phase as it emerges at the j-th ji 5
port relative to the phase of the incident wave at the i-th port. For example, the phase of the S 11 parameter of a very short (zero-length) transmission line shorted at the end is arg( S 11) = 180, indicating the phase reversal of the incident electric field (or the incident voltage) at the short. In another example, the phase of the transmission coefficient S 21 of a loss-free transmission line which is half a wavelength long, is arg( S 21) = 180. 2. Measurements with a VNA The network analyzer generates a sinusoidal signal, the incident wave, which is applied to each port of the device, one port at a time. When one port is excited, all others are matched with the standard system impedance of 50 Ω and the outgoing waves are being measured. Provided the device is linear, all of these waves are at the same frequency as the excitation. A scalar network analyzer measures only the amplitude ratio of the incident and the outgoing waves, i.e., it provides only the magnitudes of the scattering parameters. A vector network analyzer (VNA) is a much more complicated instrument, which can also provide the phase difference between the incident and the outgoing waves, thus measuring the S-parameter phases as well. The availability of vectorial information about the microwave circuit opens many possibilities, including: (a) plotting the input impedance of a 1-port device on a Smith chart, and (b) emulating time-domain measurements through an inverse Fourier transform of a very wideband measurement. The architecture and the basic principles of operation of the VNA are considered during the lectures. Here, we only emphasize that unlike low-frequency test instrumentation, the VNA needs to be calibrated before each measurement. This is necessary in order to compensate for systematic measurement errors in the test instrument with the greatest possible precision. Also, the calibration allows for the compensation of the effects of the connecting cables, connectors and adapters, so that the measured S-parameters describe the device itself, not the device together with the cables connecting it to the VNA. For 1-port measurements, 1-port calibration must be performed. The calibration method is termed the OSM (Open-Short-Matched) cal technique (also known as OSL or SOL, for Open- Short-Load or Short-Open-Load). This is because the calibration consists of three separate measurements on known terminations: an OPEN, a SHORT, and a MATCHED (50-Ω load) termination. Based on the results of these measurements, the instrument can derive the measurement errors, which include not only the internal instrument errors but also the influence of the cable attached to the port and its connector. These measurement errors are then deembedded from each subsequent device measurement. In this module, the students will perform 1-port measurements and, therefore, the VNAs must undergo 1-port calibration. Finally, we should mention two excellent resources describing the principles of operation, the calibration methods and the functionality of modern VNAs: M. Hiebel, Fundamentals of Vector Network Analysis, 5 th ed. Rohde&Schwarz, Germany, 2011. J.P. Dunsmore, Handbook of Microwave Component Measurements: with Advanced VNA Techniques. Wiley, UK, 2012. 6
1. Set up Stimulus II. PROCEDURE Sweep Type: Linear Frequency Start Frequency: 500 MHz Stop Frequency: 1 GHz Frequency Points: 201 Power Level: 0 dbm (if applicable, Power Slope: 0 db/ghz) Trigger: Continuous Frequency Offset: Off Sweep Time 1 (check and record for the Agilent VNAs only): ms 2. Set up Response Measurement: S 11 Format: LogMag (you will be changing this later) IF Bandwidth: 2 1 khz Averaging: OFF (you will be changing this later) 3 Smoothing: OFF (you will be changing this later) 4 3. Set up Scale Set to Auto Scale (you will be changing this later) 4. 1-Port Calibration Make sure the cable with an SMA 5 connector is attached to Port 1 of the VNA. Prepare the kit of SMA calibration standards: Open, Short and Load (50 Ω) terminations. For an Open, leave the cable open. [Note: For high-quality measurements, an Open standard should be used.] Select the proper type of cal kit. Select Calibrate/Full 1-Port Calibration. Attach the Open (or leave cable open) and press Open. Repeat for Short and Load. Ensure that Correction (in the Calibration menu) is ON. Once done with the calibration, re-attach the Open (or leave cable open) and change the 1 The VNAs usually sets automatically the required frequency-sweep time for the user-defined IF bandwidth. However, when measuring devices with unusually long settling times, it may be necessary to manually adjust the frequency-sweep time to longer durations. 2 IF (intermediate frequency) bandwidth is the bandwidth of the IF filter in the superheterodyne receiver. It is also known as the measurement bandwidth. Smaller IF bandwidths result in lower noise levels of the measurement but also in longer measurement times. Choosing too large an IF bandwidth may result in a loss of detailed information with respect to frequency. This is why the IF bandwidth must be orders of magnitude smaller than the frequency selectivity of the measured device. 3 The Averaging option instructs the instrument to display the averaged result over the last N measurement, where N is user-defined. Typical values for N are around 5 to 10. This option is very useful when measuring weak unstable signals. 4 The Smoothing option instructs the instrument to smooth out the response over a user defined frequency window (the smoothing aperture). This option is useful in reducing the noisy behavior of a response as a function of frequency. 5 SMA stands for SubMiniature version A. 7
Format of the S 11 response to Smith chart. Use the Port Extension option to fine-tune the virtual cable length of the port so that an open-circuited cable would exactly reside at the Γ= 1 point on the Smith chart. Export the Smith chart plot of the measured S 11 of the Open termination and insert in your Report. Mark with an x the point that corresponds exactly to S 11 =Γ= 1 for easy visual comparison. Is the reflection coefficient S 11 of the Open termination exactly equal to 1 at all frequencies with the properly tuned Port Extension? Describe what happens with the S 11 locus of the Open termination when you increase/decrease the length of the Port Extension. 8 Now test your calibration and port extension with the Short, again observing the reflection coefficient on the Smith chart. Export the Smith chart plot of the measured S 11 of the Short termination and insert in your Report. Mark with an x the point that corresponds exactly to S 11 =Γ= 1 for easy visual comparison. Now test your calibration and port extension with the 50-Ω Load termination, again observing the reflection coefficient on the Smith chart. Export the Smith chart plot of the measured S 11 of the 50-Ω Load termination and insert in your Report. Mark with an x the point that corresponds exactly to S 11 =Γ= 0 for easy visual comparison. With the 50-Ω Load termination still attached, change the Format of the response to LogMag (in the Response menu). Then enable Averaging. Set the Averaging values to 10, 20, 50 and observe the effect on the displayed curve. Does the curve become more stable in time as you increase the averaging value? Is the time of the measurement affected and how? Leave the Averaging at the value 10. Next, enable Smoothing and increase the Smoothing Aperture to 10% and then to 20%. What is the effect of on the response vs. frequency? Disable the Smoothing and the Averaging options.
5. Measuring 1-port Devices The following 1-port components are provided: 1) carbon resistor (mounted on a coaxial SMA connector) 2) RF chip capacitor (mounted on a coaxial SMA connector) 3) tiny coil (mounted on a coaxial SMA connector) 4) 3 db pad 5) 1-GHz dipole antenna 6) 1-GHz folded dipole antenna. 9 For each of these components, measure S 11 and observe the response in the following formats: (a) linear-scale magnitude ( S 11 ) (b) logarithmic-scale magnitude ( 20 log 10 S 11 ) (c) angle ( S11 ) (d) Re S 11 and Im S 11 (e) Smith chart Note: When measuring the antennas, mount them on a stand and try to point them away from nearby objects. Place your hand near or on the antenna. Does the reflection coefficient of the antenna change? Why do you think this is happening? _ Export the Smith charts for all of these components and include them in your Report. In all formats, try the use of a Marker and observe the accurate readouts at different frequencies. Answer the following questions together with an explanation of the observation: A. Is the resistance of the carbon resistor constant with frequency? B. Does the resistor have parasitic capacitance and/or inductance? C. In your opinion, what are the parasitics due to? D. Is the capacitance of the chip capacitor constant with frequency? E. Does the capacitor have loss? F. Is there a frequency range where the capacitor behaves like an inductor?
G. Is there a frequency where the capacitor has a resonance? 6 If so, does it present a short circuit (series resonance) or an open circuit (parallel resonance)? H. Is the inductance of the tiny coil constant with frequency? I. Is the coil lossy? J. Is there a frequency range where the coil behaves like a capacitor? K. Is there a frequency where the coil has a resonance? If so, does it present a short circuit (series resonance) or an open circuit (parallel resonance)? L. What is the complex reflection coefficient S 11 (magnitude and phase) when port 2 of the 3 db pad is: (a) left open, (b) terminated with a short, and (c) terminated in a matched (50 Ω) load? Explain the results in these 3 cases. 10 III. REVIEW QUESTIONS 1. What is the magnitude of the incident wave a 1 for a system impedance of Z 0 = 50 Ω if the RMS value of the incident voltage is V 0 + = 1 mv? 2. Express in watts the power level of 0 dbm. 3. A loss-free transmission line, which is quarter-wavelength long, is terminated with an OPEN. What is its complex reflection coefficient S 11? 4. A 3-dB pad is a microwave 2-port device, which, ideally, does not reflect back any power while at the same time reduces the transmitted power by 3 db. What is the magnitude of the transmission coefficient S 21 of the 3-dB pad (on a linear scale, i.e., not in db)? 5. On a Smith chart, when the frequency increases, the impedance point moves along the locus of S 11 (choose one) clockwise counterclockwise. 6 At resonance, a component exhibits purely resistive/conductive impedance/admittance.
Smith charts of: 1. OPEN Termination 2. SHORT Termination 3. 50-Ω Termination (or LOAD) 4. Carbon Resistor 5. RF Chip Capacitor 6. Tiny Coil 7. Dipole 8. Folded Dipole 9. 3-dB pad terminated with a 50-Ω load 10. 3-dB pad terminated with a SHORT 11. 3-dB pad terminated with an OPEN ATTACHMENTS 11