Study of network analyzer for measurement of SWR, reflection coefficient and ‘S’ parameters.

Aim: Study of network analyzer for measurement of SWR, reflection coefficient  and  ‘S’ parameters.

Equipment: Network Analyzer

Theory:

Network analyzers characterize the impedance or S-parameters of active and passive networks, such as amplifiers, mixers, duplexers, filters, couplers, attenuators. These components are used in systems as common and low cost as a pager, or in systems as complex and expensive as a communications or radar system. Components can have one port (input or output) or many ports. The ability to measure the input characteristics of each port, as well as the transfer characteristics from one port to another, gives designers the knowledge to configure a component as part of a larger system.

Types of network analyzers

Vector network analyzers (VNAs) are the most powerful kind of network analyzer and can measure from as low as 5 Hz to up to 110 GHz. Designers, and final test in manufacturing, use VNAs because they measure and display the complete amplitude and phase characteristics of a network. These characteristics include S-parameters, transfer functions, magnitude and phase, standing wave ratios (SWR), insertion loss or gain, attenuation, group delay, return loss, and reflection coefficient.

VNA hardware consists of a sweeping signal source (usually internal), a test set to separate forward and reverse test signals, and a multichannel, phase-coherent, highly sensitive receiver. In the RF and microwave bands, typical measured parameters are referred to as S-parameters, and are also commonly used in computer-aided design models.

Scalar network analyzers A scalar network analyzer (SNA) measures only the amplitude portion of the S-parameters, resulting in measurements such as transmission gain and loss, return loss, and SWR. Once a passive or active component has been designed using the total measurement capability of a VNA, an SNA may be a more cost-effective measurement tool for the production line to reveal out-of-specification components. While SNAs require an externalor internal sweeping signal source and a signal separation test set, they only need simple amplitude only detectors, rather than complex (and more expensive) phase coherent detectors.

                                

 Basic Block Diagram of Network Analyzer

                  

In order to measure the incident, reflected and transmitted signal, four sections are required:

1.      Source for stimulus

2.      Signal-separation devices

3.      Receivers that down convert and detect the signals

4.      Processor/display for calculating and reviewing the results

Source: The signal source supplies the stimulus for our stimulus-response test system. We can either sweep the frequency of the source or sweep its power level. Traditionally, network analyzers used a separate source. These sources were either based on open-loop voltage-controlled oscillators (VCOs) which were cheaper, or more expensive synthesized sweepers which provided higher performance, especially for measuring narrowband devices. Excessive phase noise on open-loop VCOs degrades measurement accuracy considerably when measuring narrowband components over small frequency spans.Signal Separation: The next major area we will cover is the signal separation block. The hardware used for this function is generally called the “test set”.

The test set can be a separate box or integrated within the network analyzer. There are two functions that our signal-separation hardware must provide. The first is to measure a portion of the incident signal to provide a reference for ratioing. This can be done with splitters or directional couplers. Splitters are usually resistive. They are non-directional devices and can be very broadband. The trade-off is that they usually have 6 dB or more of loss in each arm. Directional couplers have very low insertion loss (through the main arm) and good isolation and directivity. They are generally used in microwave network analyzers, but their inherent high-pass response makes them unusable below 40 MHz or so. The second function of the signal splitting hardware is to separate the incident (forward) and reflected (reverse) traveling waves at the input of our DUT. Again, couplers are ideal in that they are directional, have low loss, and high reverse isolation. However, due to the difficulty of making truly broadband couplers, bridges are often used instead. Bridges work down to DC, but have more loss, resulting in less signal power delivered to the DUT.

Detector Types: The next portion of the network analyzer we’ll look at is the signal detection block.

There are two basic ways of providing signal detection in network analyzers. Diode detectors convert the RF signal level to a proportional DC level. If the stimulus signal is amplitude modulated, the diode strips the RF carrier from the modulation (this is called AC detection). Diode detection is inherently scalar, as phase information of the RF carrier is lost. The tuned receiver uses a local oscillator (LO) to mix the RF down to a lower “intermediate” frequency (IF). The LO is either locked to the RF or the IF signal so that the receivers in the network analyzer are always tuned to the RF signal present at the input. The IF signal is bandpass filtered, which narrows the receiver bandwidth and greatly improves sensitivity and dynamic range. Modern analyzers use an analog-to-digital converter (ADC) and digital-signal processing (DSP) to extract magnitude and phase information from the IF signal. The tuned-receiver approach is used in vector network analyzers and spectrum analyzers.
Dynamic Range and Accuracy: This plot shows the effect that interfering signals (sinusoids or noise) have on measurement accuracy.

The magnitude error is calculated as 20*log [1 ± interfering-signal] and the phase error is calculated as arc-tangent [interfering-signal], where the interfering signal is expressed in linear terms. Note that a 0 dB interfering signal results in (plus) 6 dB error when it adds in phase with the desired signal, and (negative) infinite error when it cancels the
desired signal. To get low measurement uncertainty, more dynamic range is needed than the device exhibits. For example, to get less than 0.1 dB magnitude error and less than 0.6 degree phase error, our noise floor needs to be more than 39 dB below our measured power levels (note that there are other sources of error besides noise that may limit measurement accuracy). To achieve that level of accuracy while measuring 80 dB of rejection would require 119 dB of dynamic range. One way to achieve this level is to average test data using a tuned-receiver based network analyzer.

 Detailed block diagram

 

S parameter measurement using a network analyzer
S parameter measurement using a network analyzer:

The Network Analyzer is used to measure S parameters (scattering parameters) of one or more port devices.  The S parameters are very useful to characterize devices at high frequencies where the traditional measurements are very difficult to measure.  These parameters are defined in terms of traveling waves moving along transmission lines and they completely characterize the behavior of one of more port devices.  The S parameters are simple to use because

ü  Matched loads are used in their determination.  At high frequencies matched loads are relatively easy to realize, while the short and open circuits required for the traditional low frequency parameters are much more difficult to achieve and furthermore, are more likely to make an active device unstable.

ü  When only the magnitudes of the S parameters are required, it is not necessary to be concern with the position of the reference plane, planes at which the DUT (device under test) begins and the connecting test network ends.  The reference planes only affects the phase of the S parameters.

           

Consider the two-port device in the figure.  The S parameters are define as

 

where

            The analyzer has an RF signal source that produces an incident signal that is used as a stimulus to the device under test.  Your device responds by reflecting a portion of the incident signal and transmitting the remaining signal.  Figure 2 shows how a DUTresponds to an RF source stimulus.

Figure 2: DUT Response to an RF Signal

The network analyzers require to be calibrated with a set of standards (OPEN, SHORT and LOAD) terminations.  This calibration will enhance the precision of the measurements discarding any losses due to cables and adapters to the DUT.

Measurement calibration is a process that improves measurement accuracy by using error correction arrays to compensate for systematic measurement errors.  Measurement errors are classified as random, drift and systematic errors.  Random errors, such noise and connector repeatability is not correctable by measurement calibration.  Also, drift errors, such as frequency and temperature drift are not correctable by calibration.

Systematic errors, such as tracking and crosstalk, are the most significant errors in most RF measurements, which can be corrected by calibration. Repeatable systematic errors are due to system frequency response, isolation between the signal paths and mismatch and leakage in the test setup.  Mismatch error result from differences between the DUT's port impedance and the analyzer's port impedance.  If the DUT is not connected directly to the port, the mismatch errors due to cables, adapters, etc. are considered part of the DUT mismatch errors.

PROCEDURE

Calibration Steps for the RF Amplifier

1.   Enter Measurements Parameters

a.      Set input power level to avoid amplifier saturation.

1.      Press POWER hardkey

2.      Press Level softkey -2, and dBm.

b.      Set desired frequency range.

1.      Press the FREQ key to access the frequency softkey menu.

2.      Change the low end frequency to 10 MHz, press Start10 MHz

3.      Change the high end frequency to 100 MHz, press Stop100 MHz

4.      You can also set the frequency range by using the Centerand Spansoftkeys.  Press the Center and enter 55 MHz and press Span and enter 90MHz.

c.       Set desired number of measurement points.  This allows selection of the number of measurement points in a sweep.  As the number of points increases, frequency resolution increases and sweep speed decreases.

1.      Press the MENU hardkey

2.      Press the Number of Points softkey and enter 801.

2.   Performing Transmission Response Calibration

a.      Select calibration method and calibration kit.

1.      Press CAL Enhanced Response.

b.      Connect the four standards open, short, load and through cable in each port as shown in figure 4.

1.      The instrument will prompts you to connect the four standards

2.      Press Measure Standard after connecting each standard.

Figure 4: Calibration Standards

3.      The instrument will measure each standard and then calculate the new calibration coefficients.  The message "Calibration complete" will appear.

4.      Save the calibration into memory.

a.         Press SAVE RECALL, Select Disk, Non-Vol RAM Disk.

b.         Press Prior Menu, Define Save, Cal ON

c.          Press Prior Menu, Save State to save the instrument state file.  The filename appears on the screen as STATE#.STA (where # is a number the analyzer selects from 0 to 999).  

Performing RF Amplifier Measurements

1.   Connect the DUTas illustrated in figure 5 (RF OUT to amplifier’s input and RF IN to amplifier’s output)

2.   Measure the S₁₁, S₂₁ in Log format

a.      Transmission (S₂₁) and Reflection(S₁₁)

1.      Press MEAS1, Transmissn, FORMAT, Log Mag, SCALE, Autoscale

2.      Press MEAS2, Reflection, FORMAT, Log Mag, SCALE, Autoscale

3.      Press DISPLAY, More Display, Split Disp FULL split

4.      Use markers to interpret the data

5.      Print the amplifier’s frequency response.

Figure 5: Equipment Setup for a Transmission Response Measurement

b.      Use Smith Chart to measure reflection (S₁₁)

1.      Press MEAS1, Reflection, FORMAT, SmithChart, SCALE, Autoscale

2.      Press MEAS1, Reflection, FORMAT, SmithChart, SCALE, Autoscale

3.      Use markers to interpret the data.

4.      Print the Smith chart.

3.   Connect the DUTas illustrated  (RF OUT to amplifier’s output and RF IN to amplifier’s input)

4.   Measure the S₂₂, S₁₂ in Log format

a.      Transmission (S₁₂) and Reflection(S₂₂)

1.      Press MEAS1, Transmissn, FORMAT, Log Mag, SCALE, Autoscale

2.      Press MEAS2, Reflection, FORMAT, Log Mag, SCALE, Autoscale

3.      Press DISPLAY, More Display, Split Disp FULL split

4.      Use markers to interpret the data.

5.      Print the amplifier’s frequency response.

b.      Use Smith Chart to measure reflection (S₂₂)

1.      Press MEAS1, Reflection, FORMAT, SmithChart, SCALE, Autoscale

2.      Press MEAS1, Reflection, FORMAT, SmithChart, SCALE, Autoscale

3.      Use markers to interpret the data.

4.      Print the Smith chart.

VSWR:

VSWR, or voltage standing wave ratio, is a measure of how well the components of the RF network are matched in impedance. When the impedances are improperly matched, you lose signal power, which results in weak transmissions, poor reception or both.

Maximum power transfer between two system components occurs when their respective impedances are matched. If the impedances are not identical, some RF power will be reflected back, resulting in a reduction in the amount of power delivered to the load. These reflections cause voltage standing waves.

VSWR is defined as the ratio of the maximum voltage to the minimum voltage in the standing wave. The larger the impedance mismatch, the larger the amplitude of the standing wave.

A perfect impedance match would cause no voltage standing wave, so the ratio of the maximum voltage to the minimum would be 1 (1:1).

Most RF systems have a characteristic impedance of 50Ω. All of the devices in the transmitter and receiver sections are designed to have input and output impedances of 50Ω. This includes the coaxial cables that are used to interconnect the devices. These devices include multiplexers, bandpass filters, duplexers, low-noise amplifiers, combiners, power amplifiers etc.

Although the concept of VSWR is easy to comprehend, it is extremely difficult to measure directly. For that reason, you need to measure other parameters, such as return loss and then from that calculate the magnitude of the reflection coefficient, ρ (lower case Greek letter Rho) which can then be used to calculate VSWR.

Return loss is the difference in power (expressed in dB) between the incident power and the power reflected back by the load due to a mismatch. It can be measured directly in dB with a Spectrum Analyzer or Network Analyzer along with a few key components. It is expressed as:

Return loss (RL) = -10log(Preflected /Pincident )

A perfect match would result in no reflected power (as it is all delivered to the load), so the return loss would be infinite. Conversely, an open circuit would reflect back all power, so the return loss would be zero. When dealing with return loss, the higher the value, the better the impedance match.

Once the Return Loss is known, the next step is calculate ρ :

By definition, ρ = √(Preflected /Pincident )

But since RL = -10log(Preflected /Pincident ) we can manipulate this expression to get ρ as a function of RL.

-RL/10 = log(Preflected /Pincident )

Then raise both sides to the power of 10:

10-RL/10 = 10(log(Preflected /Pincident )) = (Preflected /Pincident )

Thus we get:

(Preflected /Pincident ) = 10-RL/10

Now we take the square root of each side:

√(Preflected /Pincident ) = √10-RL/10 = 10-RL/20

Thus ρ = 10-RL/20

VSWR can then be calculated using the following formula:

VSWR = (1+ ρ )/(1- ρ )

The Return Loss can be measured in several different ways using a directional coupler along with some level measuring device such as a common Spectrum Analyzer/tracking generator, power meter or Network Analyzer. The directional coupler is first set up with a short or open circuit which reflects all of the power, so that Preflected /Pincident. Substituting the load in question for the short circuit allows the actual reflected power to be measured. The difference, in dB, between the power reflected with a short and the power reflected by the load at any given frequency becomes the RL for that frequency. Next, ρ can be calculated and then VSWR can be calculated

You also can use a time domain reflectometer to measure the reflection coefficient and apply that value to calculate VSWR.

Keep in mind that the reflection coefficient, Γ (upper case Greek letter Gamma), and the magnitude of the reflection coefficient, ρ (lower case Greek letter Rho) are related but not the same.

ρ = | Γ |

Γ is a complex number with real and imaginary components. Γ is a function of the complex impedance of the load and the characteristic impedance of the transmission line. It is given by Γ = (Z1-Z0)/(Z1+Z0) where Z1 is the complex impedance of the load and Z0 is the characteristic impedance of the transmission line. Z1 is not easily measured directly.

The reflection coefficient is a voltage ratio and must be squared to be used for power calculations. It is sometimes easier to think of reflected power in terms of reflection coefficient than in return loss. Reflected power is equal to the incident power multiplied by the reflection coefficient squared. Procedure : I. Network Analyzer Settings Turn the Power On Set the Frequency for Measurements (600 MHz) Calibrate the NA, at the end of the cable, and verify it. II. Prepare the Automated Slotted Coaxial Line (ASCL) System With the power OFF, connect the cable from port #1 of the network analyzer to the input of the slotted line. Connect the cable from port #2 to the probe carriage. Make sure all the cables are positioned to allow the probe carriage to travel unrestricted along the entire length of the machine. Move the probe carriage, manually, down the entire slot to ensure this. Failure to do this, will result in damage to the motor and hardware. Turn the power ON for the ASCL. The probe will move to the home position if it is not already there. III. Generate the SW plot Turn on computer and click on the halfstep.vi icon. The User Interface Screen will open The ASCL will automatically record and plot the SW pattern on screen. (ii) Plot a Normalized SW pattern Click on RUN. ( button in the toolbar ) PC takes control of NA From the MODE SELECTION box, choose AUTOMATIC Choose RESOLUTION as MEDIUM Choose LOAD IMPEDANCE (Z>Z0 or Z<Z0 or Z=Z0 or Complex) Set DUAL PLOTTING to OFF Click on START. Click on OK when Dialog box appears to verify load. SW Pattern is generated as the probe moves down the slotted line. The normalized SW pattern will be plotted on the screen when it reaches the end. (iii) Save Data Choose YES in the dialog box for saving data. (Ignore any ‘Timeout Expired’ error messages) Insert a disk and choose Drive A Name the file (name.txt)  (iv) Measure SWR on the Network Analyzer On the NA panel, do the following LOCAL SYSTEM CONTROLLER (ignore message) MEAS REFLECTION FORMAT SWR (Record the SWR) (v) To take control of the NA through LABVIEW, click on ‘Control Devices’ button. This can also done by ABORT and RUN. Conclusion: