Definition of Scattering Parameters
Cassini Measurement Hardware
Two Port Error Model
S Parameters, abbreviated from Scattering Parameters, are fundamental RF terms used for characterizing RF/Microwave devices and RF/Microwave signal networks. The following lesson will define S Parameters, describe the measurement process and concepts associated with S Parameter measurements, describe how the ATE System performs S parameter measurements and discuss two port error correction of systematic errors.
S Parameter Definition
S Parameters or Scattering parameters (S11, S12, S21, S22) define the relationship between the incident, transmitted and reflected signals at the inputs and outputs of the device under test. The examples and equations shown are for a two port RF device.
a1 is the incident signal applied in the forward direction to the input port (port 1).
a2 is the incident signal applied in the reverse direction to the output port (port 2).
b1 is the energy out of port 1 that is equal to the sum of the reflected energy from the a1 signal applied to port 1 and the energy transmitted through the device from the a2 signal applied to port 2.
b2 is the energy out of port 2 that is equal to the sum of the reflected energy from the a2 signal applied to port 2 and the energy transmitted through the device from the a1 signal applied to port 1.
Measuring 2 Port S Parameters
To determine the four S Parameters, we first terminate port 2 with a Z0 load eliminating the a2 signal. The resulting equations yield S11 and S21. S11 is the ratio of b1/a1 and S21 is the ratio of b2/a1, when a2 is zero. S11 is equivalent to the reflection coefficient, Γ (gamma). Please notice that Γ is defined as Vinc/Vrefl = b1/a1. Similarly, S21 is equal to the forward transmission coefficient.
S Parameters use a numbering convention that the first number represents the RF port where the energy emerged from the device and the second number is the RF port where the incident energy is applied to the device. Thus, S21 is the ratio of the energy emerging from port 2 to the energy incident at port 1. Gain or loss is indicated by values greater or less than unity.
Measuring 2 Port S Parameters
By placing the source at port 2 and terminating the input with a Z0 load, the a1 term is now zero and S22 and S12 can be determined. Notice that the S Parameters are referenced to the Z0 impedance (typically 50 ohms) of the network analyzer.
Testing an Attenuator
One of the advantages of S Parameters is that they are intuitive. S21 is simply the forward gain or loss of the device in linear units. For the 20 dB attenuator shown, we see that the loss through the attenuator is equal to an S parameter voltage ratio of 0.1. Since S Parameters arc complex parameters, there is a phase angle term as well as a magnitude term associated with each S parameter. The SWR of the device is equivalent to the S11 or input voltage reflection coefficient of 0.09.
S Parameter Flow Graph
This is a flow graph representation of a two port device, such as the attenuator from the previous example. The input port has two nodes: one representing the incident "a" wave and one for the emerging "b" wave. Lines that connect nodes are called branches. Each branch has an arrow and a value corresponding to an S parameter. Energy will only flow in the direction of an arrow. We will use these Flow Graph representations to describe the vector calibration process that gives the RI ATE platform its accuracy.
One Port S Parameter Measurement Model
By applying well defined vector calibration techniques, we can characterize the stable and repeatable systematic errors and mathematically remove these errors from the measurement process, improving the system’s overall measurement performance. This process is often referred to as S Parameter error correction. The one port measurement model shown identifies the three major systematic errors associated with one port measurements. D represents directivity errors, TR represents tracking errors and MS represents source match errors. A complete two port model will be presented later.
Directivity errors are caused by signals other than the signal reflected off of the DUT detected at the reflection measurement arms of the directional separating device in the S Parameter measurement hardware. These error signals are caused by imperfections in the directional separating devices used in the Test Head and impedance mismatches of the adapters or test cables that physically connect the device under test to the Test Head. The errors combine vectorally with the true reflection coefficient (S11 A for the actual value we are seeking) to yield an inaccurate value for the measured data S11 M (M for what is actually measured). We call the combined errors "overall directivity".
Reflection Tracking Errors
Reflection tracking errors are a composite of the frequency response of the directional separating devices in the Test Head (tracking), the test cables, switches, connectors and the microwave mixers in the System Receiver.
Source Match Errors
When a signal is reflected back off the test device into the test system, the signal does not see an ideal load due to all of the small mismatch errors caused by imperfect connections, switches, and transitions in the system Test Head. An error loop is formed with the signal bounces back and forth. This error is related to the product of mismatch terms and it is only a major factor when the test device has a large mismatch.
1 Port Calibration & Vector Error Correction
The impact of performing calibration and vector error correction to mathematically eliminate systematic errors (even for one port devices) is significant, as you can see by the graph. The importance of vector error correction for multi-port devices is even more critical.
Two Port Error Models
Transmission Measurements add more complexity:
The two port transmission measurement model identifies four major systematic errors: crosstalk (C), source match (MS), load match (ML) and transmission frequency response (TT). The crosslalk (C) error term is due to signals leaking around the DUT. The leakage error may become significant when the transmitted signal level is reduced substantially by the test device, such as in high loss devices.
We can also see that any load mismatch at the output of our test device has the potential of adding errors to our input port reflection measurement by causing signals to be reflected back through the device. The error contribution is a function of both the forward and reverse transmission characteristics of the DUT and the load match presented to the DUT. We will refer to this term as the "load match" of our test system.
Two Port Error Model
The transmission measurement model is shown in the above flow graph. Notice the interaction of the source match (MS) with S11 A, the load match (ML) with S22 A, the transmission frequency response error (TT) with S21 A and the source match and load match with S12 A. This model shows that in order to accurately extract S21 A data, we need to also know accurately S11, S12 and ,S22.
2 Port Calibration & Vector Error Correction
Characterize Systematic Errors
Remove Systematic Errors from Measurement
Reflection Cal: MS, D, TR
Thru Connection : TT, ML
Isolation Measurement : C
By performing a full two port S Parameter measurement calibration, we can characterize and mathematically remove the effects of the systematic errors in the RI 7100A or Cassini platform. All four measured S Parameter terms are needed to solve for the error correction equations, therefore we must measure all four S Parameters (both magnitude and phase) in order to determine any of the actual S Parameter values.
The traditional two port calibration approach always requires a through measurement to accompany the one-port reflection calibration that determines directivity, frequency response, and source match. Traditionally, only ratios are used in the measurement process but RI test methods use a newer approach that takes absolute voltage values at each measurement point (a1, b1, a2, b2). This gives you the option of using one port calibrations if the device has high isolation between its ports (i.e. active amplifier devices or mixers) without needing a through standard or to use a through connection to characterize transmission frequency response and load match. This technique works well for frequency translation devices and multi-port devices that would prove to be very difficult to calibrate if a through measurement was needed.
4 Port Test Configuration for S Parameters
The block diagram and test configuration presented is a typical two port S Parameter measurement configuration for the RI Testset. The two port active Device Under Test (DUT) is shown connected to RF ports RF3 and RF6. The RF stimulus source (Source1) is routed by the matrix modules through the low loss cables into the Source1 input port of the RF Testset. The RF stimulus signal is routed through the Testset switches to the DUT’s RF input connected to port RF3. The resulting incident and reflected signals at port RF3 and transmitted and reflected signals at port RF6 are separated by the directional couplers connected to port RF3 and port RF6. RF3 and RF6 were chosen to take advantage of the maximum isolation through the RF Testset since each of those ports are connected to different switches providing extra isolation (over 100 dB vs Approx 60 dB). The electronic switches (connected to the coupled arms of port RF3 and RF6 directional couplers) individually route these coupled signals through a second switch (for isolation), a RF Solid State step attenuator, and a RF preamplifier to the REC port which travels through low loss microwave cables back to the System Matrix and to the single channel System Receiver for signal processing. The normal operating mode of RI ATE Systems use a bi-state load pull approach, instead of reversing the DUT or reversing the RF stimulus signal’s direction to measure the S22 and S12 terms. This unidirectional S Parameter measurement approach is especially useful for characterizing unidirectional active devices, such as power amplifiers, at high RF signal levels. To create the bi-state loads, the RF Testset uses customized high speed electronic switch loads that are connected to the thru path of each of the directional couplers. Follow the thru path of the directional couplers to the mechanical switch and an electronic switch to the bi-state loads L1 and L2. A standard bidirectional S-parameter mode is also supported for passive, low gain or low loss device measurements.
Measurement Configuration for S Parameters
The signals received by the System Receiver (at its 0.005 - 2 GHz or 0.1 - 20 GHz INPUT port) are fundamentally down converted to the 21.4 MHz IF frequency using the external System Local Oscillator connected to the LO In port. The IF signals are conditioned (attenuated, filtered or amplified) and sent to the complex/synchronous quadrature detectors. The complex detector splits the received signal into two equal amplitude and equal phase signals and mixes one signal with a 21.4 MHz signal in-phase with the System Receiver’s internal 21.4 MHz SOURCE to create the "I" (in-phase) signal component and mixes the other signal with a 21.4 MHz signal which is 90° out of phase with the 21.4 MHz SOURCE to create the Q (quadrature) signal component. The resulting signals are low pass filtered and sampled by high speed sample and hold circuits. The high accuracy analog to digital (A to D) converter digitizes the sampled I and Q signal components and sends the digitized data over the RIFL II bus to the System Computer for processing. The 21.4 MHz SOURCE signals are generated from (and slaved to) the system wide 10 MHz frequency reference/time base distributed by the RIFL II bus.
Traditional Dual S-parameter receivers need an active reference channel (with all the drift and errors associated with it) to measure all the S Parameters. The RI 7100A and Cassini, however, use an innovative implied reference technique based of the stability of the Synthesized Microwave Signal generators to switch a single channel receiver to perform all the S Parameter measurements. This allows for stable long term performance without the need for constantly recalibrating the receiver due to drift. The RI Microwave Test System provides high speed, high accuracy S Parameter measurements, measuring all four S Parameters in less than 250 μsec with approximately 34 dB of residual directivity and tracking errors less than ± 0.1 dB and ± 1.0° at the RF port connections. This performance is always a function of the connector interfacing required by the DUT and may degrade based on the quality and stability of that interface.
S-Parameter Measurement Variations