S-Parameters

This function group is for various computations with S-Parameters.

S-Parameter Conversions

This tab is used to computer conversion of units for the S-Parameters.

 

dB/Deg

I entered the S11,S21,S12 and S22 in units of dB and Degrees and in the next figure blow I computed the linear units of S-Parameters.

Figure 60 – Spar dB/Deg Input

Figure 61 – Spar Rect/Linear Units

In this screen I show the conversion from dB/Deg to Impedance in Ohms.

Figure 62 – Spar Impedance

In this screen I show the conversion from dB/Deg to Admittance in Mhos or Siemens

.

Figure 63 – Spar Admittance

Network Transforms

This tab is used to convert any network parameter to any network parameters.

Figure 64 – Network Parameter Transforms


S-Parameters Embedding

This function is used to embed or combine the S-Parameter responses of two 2-port network elements together. In the case shown I took a 6dB attenuator with -14dB return loss S11, S22 and -6dB loss forward and reverse S21 and S12 and combined it with a simulated amplifier with -20dB return loss S11/S22, -20dB rev S12 and 20dB fwd gain S21. This gives a combined network response of -12.9 S11, 14.17dB S12, -25.82dB S12 and -10.85db S22. We will see these values again in the De-Embed function. Enter the S-Parameters and Press Calculate to compute and display. Clear to reset and reenter value to retry and Close to Quit.

 

Figure 65 – Spar Embedding


S-Parameters De-Embedding

This function is used to de-embed or remove the S-Parameter response of one 2-port network from the combined elements response to get the remaining sub-network. We will take the values of the case shown in Embedding. The process is to take the response of the element to be removed and find the Anti-network of it and embed that with the combine response to get the remaining network response.

 

I took a 6dB attenuator with -14dB return loss S11, S22 and -6dB loss forward and reverse S21 and S12 and combined it with a simulated amplifier with -20dB return loss S11/S22, -20dB rev S12 and 20dB fwd gain S21. This gives a combined network response of -12.9 S11, 14.17dB S12, -25.82dB S12 and -10.85db S22. In this De-Embed function. Enter the S-Parameters for the combined network in the B matrix and the attenuator in the N Matrix above. We wish to remove the attenuator from the combine response to get the base amplifier response.

After the Attenuator values in dB/Deg are entered select the “A” network to be the one removed and press the Calculate in the Upper 1/N Anti-Network section. This calculates the Anti-Network of the N matrix and will copy to the A matrix position in the lower De-Embed section. Now the user can select the Calculate in the lower De-Embedding section. The attenuator in this case, will be removed from the combined network matrix B to give the original amplifier response as can be seen in Matrix C. This gave an answer of 19.999dB S21, -19.99 S11/S22 and -20dB S12, all within rounding error for the truncation of the input values. Press Clear to reset and reenter value to retry and Close to Quit.

 

Figure 66 – Spar De-Embedding

 


Source/Load Impedance

This tab has two functions, one for converting between gamma, S-Par S11 or S22 and Impedance. The other on the right side is for finding the source and load gamma from the source and load impedances and the network S-parameter response. Gamma In and Gamma Out are used for the gain equations and more. Enter the source and load complex impedance 0 iOhms if resistive and the S Network response. It will calculate the S11 prime and S22 prime and all the network gains (power, Available, Transducer and Unilateral Transducer). Press Calculate to compute and display. Clear to reset and reenter value to retry and Close to Quit.

 

Figure 67 – Spar Source/Load Impedance

S<>Z<>Gamma

The function on the left hand side is used to convert between S-Parameter S11 or S22 to Gamma and Impedance. Enter any one of the values and the system impedance if it needs to be modified from the default of 50 Ohms and Press Calculate to compute the others and display. Clear to reset and reenter value to retry and Close to Quit. This example I input the S11 of -14dB which is nearly 75 Ohms and 0.2 Gamma.

Figure 68 – Spar – Spar to Gamma and Z

Here I input 75 Ohms and computed the rest.

Figure 69 – Spar - Z to Spar and Gamma

This screen was an entry of 0.2 gamma and computing the rest.

Figure 70 – Spar Gamma to Spar and Z

 


Spar Re-Normalization

This function is used to convert network S-Parameter response taken in a certain system impedance, such as the typical 50Ohms of most RF instruments, and to compute the S-Parameter response in a different source and load impedance. Enter the Zsystem, Zin, Zout and S11,S21,S12 and S22 of the network and Press Calculate to compute the others and display. Clear to reset and reenter value to retry and Close to Quit.

 

In the example shown I used an amplifier with -14dB return loss S11/S22. Which is an impedance eof about 75Ohms. I also give a S21 gain of 6db and S12 of -15dB. When I calculate, you can see the with the improved match at 75 Ohms, the S11 and S22 show the improvement in match at S11=-22.19 and S22=-35dB and the increased gain at 6.48dB.

 

Figure 71 – Spar Re-Normalize

Vector Analyzer

This section performs a variety of the functions most associated with the Vector Network Analyzer. This instrument measures a complex set of values these parameters are knows as S-Parameters. This function set will perform S-Parameter conversions of units and also for impedance change of the measurement system or DUT. These functions also include ones for phase length, and all the basic calibration kit definition suite of functions. I also included the coax, waveguide and stripline calculators to make them convenient for the waveguide cutoff, the Offset Length, and other parameters.

 

Cal Kit Definition

This section covers the majority of the cal kit definition functions of Offset Loss, Offset Delay and Offset Zo.

 

Offset Loss

Offset loss is used by Agilent to characterize the loss of the calibration kit component so the VNA can model the loss. Enter the RF Loss in dB at 1Ghz, The Offset Zo calculated using Offset Zo, the physical length and the dielectric constant Er. Press calculate to perform calculation and “Clear” to clear and start over, Er defaults to 1.0.

 

Offset Delay

Offset delay is the electrical delay of the cal kit component based on it’s physical length and the Dielectric constant Er. It can also be determined from the Frequency and Phase delta. In the case shown, I entered the physical length and the frequency and used the default Er of 1.0 (air). Pressing “Calculate” it computed the Phase in degrees and the delay in nanoseconds. Press “Clear” to clear the text boxes and start over, Er defaults to 1.0.

 

Offset Zo

Offset Zo is a simplified version of the Coax impedance calculator on another tab. I am presenting the version here Agilent has in their Application notes. Enter the Inner and Outer diameter and the Dielectric Constant Er and Ur if non-unity. Press Calculate to calculate Zo in ohms or press. Clear to reset and reenter value to retry and Close to Quit.

Figure 110 – VNA Cal Kit Definitions

 

More Cal Kit

This section covers the remainder of the cal kit definition functions of C Effective, Waveguide Actual Delay and the Frequency Resolution.

 

C Effective

This function will compute the C effective for the phase shift of the cal kit standard. Enter the Phase offset, the frequency, the Zo characteristic impedance of the standard and the Cx capacitive Impedance. Press “Calculate “ to compute the C-effective in pF and press “Clear” to start over. This function again has many multifunction possibilities. Enter in the Ceff and it will figure one of the other missing values.

 

Waveguide Actual Delay

The waveguide delay figures the true delay of waveguide that changes as the frequency of operation gets closer or beyond waveguide cut-off. Use the pull down combo box to select the waveguide type, enter the delay of the waveguide when it is in TEM 01 mode and finally enter the frequency of the measurement in GHz. Press “Calculate” to figure the Actual waveguide delay in nS or “Clear” to clear text boxes and rerun.

 

 

Figure 111 – VNA More Cal Kits

 


Phase and Group Delay

This section will perform the Phase Length and delay and also the group delay.

 

Phase Delay

Phase delay is the electrical length of a device based on it phase length in degrees and dielectric constant and frequency. Enter the Phase Delay in degrees, Frequency in MHz, Dielectric Constant Er and press “Calculate” to compute and “Clear” to start over. As an addition feature if the delay in air is known it will back compute the missing Phase Delay or frequency provide the other is known.

 

Group Delay

Group delay is the rates of change of the phase vs the frequency. This is also known as the first derivative of the phase vs frequency. Enter any two of the Delta Phase in degrees change, the frequency change in MHz and press Calculate the Group Delay in nS. If you know the group delay and frequency or phase you can calculate the missing value.

 

Figure 112 – VNA Phase and Group Delay

Calibration Calculation

Frequency Resolution

The frequency resolution is a simpler version of the Frequency tool. I put this here to aid in figuring the VNA setup while working in this section. By entering any three of the four variables it will calculate the missing one. So you can use it to calculate Start, Stop, Stop frequency and or number of points. Keep in mind that the Agilent VNA like to see 51, 101, 201, 401, 801 and 1601 points. My fuller tool on another screen has features to see each frequency and even search for nearest lower, higher or closest frequency point to the trace point frequencies. So enter any three variables in MHz or points and Press Calculate to compute and display. Clear to reset and reenter value to retry and Close to Quit.

 

Residual Phase of Open and Short

This screen can be used to calculate the residual phase offsets for the open and short calibration standard coefficients for C0-C3 and L0-L3 for the respective Open and Short definitions. After the frequency portion is input and calculated the user can add the open or short coefficients and slide the Scroll bar across the frequency range and the frequency updates as will the residual phase for the open or short calibration standard. This can be used to test and refine the coefficient model across frequency.

Figure 113 - VNA Calibration Calculation Input

 

Figure 114 - VNA Calibration Calculation Initial Calc


Figure 115 – VNA Calibration Calculation Final

 

S-Parameter to Device Capacitance/Inductance

This screen is used to compute the Capacitance or Inductance value of a given S-Parameter (s11) response at a given frequency. Upper half or positive reactance will give Inductance and the lower or negative half gives Capacitive values. Enter the System Impedance, The S11 and the frequency in MHz. Press Calculate to compute, Clear to reset and try again or Close to quit and return to the main menu.

 

Figure 116 VNA S-Parameter to Inductance value

Figure 117 – VNA S-Parameter to Capacitance value


S Parameter Conversions

This section is for converting S-Parameter units from one to another. In my work we mostly use dB-Degrees for Magnitude and Angle measurements off the Vector Network Analyzer. Adding the frequency of the measurement allows one to convert to the Impedance and it’s inverse the Immitance. In this example I took an Amplifier of -14dB return loss S11 and S22 with a S21 gain of 10dB and a S12 of -10. The input impedance of the source is 52 Ohms and 55 Ohms on the load impedance.

Figure 118 – VNA S-Parameter Conversion

S Parameter Renormalize

This function will compute the Renormalized S Parameters when you convert Measured S-Parameters to another Impedance Plane for the System. Most VNA systems are 50Ohm system impedance. In many cases the impedance of the device and fixturing around it may be another impedance plane such as 75Ohm unbalanced line. In the case shown I used Zin and Zout of 75Ohms and the S-parameters of the DUT is -14dB A+S11 & S22, 6dB S21 and -20dB S12. The Renormalized S-Parameters show the match improvement for S11 and S22 which both show the improved match at 75 Ohms and the S21 shows the gain increase from the lower match loss. Press Calculate to compute, Clear to reset and try again or Close to quit and return to the main menu.

Figure 119 – VNA S-parameter Re-Normalization


Microstrip

Selecting this tab the user can perform calculation for MicroStrip line width, height from ground plane or Dielectric Thickness, Characteristic Impedance - Zo and Dielectric Constant - Er.  The user can input any three of these quantities and the program will compute the remainder and the velocity factor as a ratio of the speed of light. In addition, if the frequency of use is input then the full and quarter wavelengths are computed. I have defaulted to 1GHz frequency input.

 

Figure 120 – VNA Microstrip

Waveguide

Selecting this tab the user can perform calculation for Waveguide by giving inputs of width, height, Dielectric Constant – Er and the wave mode to compute the rest. In addition, if the frequency of use is input then the full and quarter wavelengths are computed. I have defaulted to 1Ghz frequency input. Included in the calculations are the Cut-off frequency, the Upper and Lower Operating Range and the Velocity factor of propagation. By checking the PreDef Waveguide checkbox the user gets the calculations for all the predefined waveguide. Un-checking the box allows the user to input non-standard waveguide dimensions to calculate.

 

Figure 121 – VNA Waveguide

 

Coax

This tab selection gives the user the functions to compute the characteristics of Coax Cable. The user can select from Predefined Coax types by checking the Defined Coax box or Custom Inputs by un-checking. The user can input his own variables in custom input mode. The four basic inputs are Inner Diameter (in), Outer Diameter (in), Dielectric Constant-Er and Characteristic Impedance-Zo. Input any of these three and Press the “Calculate Coax” button to compute the remaining fourth main element. The rest of the calculations are performed from the basic inputs and the Frequency Input. It computes the Cut-off frequency, Capacitance and Inductance per foot, the Time Delay, Velocity of Propagation as percent of light. With the frequency input it will add the calculation of full and quarter wavelength. I have defaulted to 1 Ghz frequency input.

Figure 122 – VNA Coax

Vector Error

This menu selection will give the operator the option of Reflection or Transmission Error analysis for Vector Network Analyzer measurements.

 

Transmission Error

This section performs the Vector Network Analyzer Transmission Error Analysis. Enter the Source Match, Load Match, Crosstalk, Transmission Tracking and Device S11, S21 and S22 in dB format. Then press “Calculate” to give the upper and lower Return Loss (RL) error bounds for the measurement of Return Loss for the device under test. Press “Clear” to re-enter or “Close” to quit.

Figure 147 – Vector Transmission Error

Reflection Error

This section performs the Vector Network Analyzer Reflection Error Analysis. Enter the Coupler Directivity, Source Match, Reflection Tracking and Device Return Loss all in dB format. Then press “Calculate” to give the upper and lower Return Loss (RL) error bounds for the measurement of Return Loss for the device under test. Press “Clear” to re-enter or “Close” to quit.

Figure 148 – Vector Reflection Error