S-parameter in LTspice

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S-parameters
Research · September 2017
DOI: 10.13140/RG.2.2.13898.67527
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2. S-parameters
Scattering parameters are defined in terms of wave variables rather than voltage and current to
get relation between input and output. S-parameters or scattering parameters are a good
analysis for microwave circuits, which have a typical frequencies range from approximately
300MHz to 1000GHz. These types of circuits consist of sources (microwave oscillators),
transmission lines (coaxial cable), waveguides, attenuators, resonators, circulators, directional
couplers, isolators, terminators, and transmitting antenna. To analyze such circuit, it can be
done through relating input and output variables of each component [1].
Considering the two-port network, the traveling waves are related to the S-parameters as
following:
[ ] [ ] [ ]
a1 and a2 are the incident waves at ports 1 and 2, respectively; and b1 and b2 are the reflected
waves.
S11 is the input return loss [dB] (input rejection ratio), S22 is the output return loss [dB] (output
return loss), S12 and S21 are off-diagonal terms represent voltage wave transmission coefficients
(reverse and forward voltage gains, respectively), while S11 and S22 are the diagonal terms
represent reflection coefficients.
The network is called reciprocal, if the transmission characteristics in either direction is the
same (S12 = S21). The network is called symmetrical, if the return losses at the input and the
output are equal (S11 = S22).
In case of matched two-port network, the reflection coefficients are zero and equal to each
other (S11 = S22 = 0).
The input reflection coefficient can be expressed in terms of the S-parameters and the load ZL
as
where is given by

3. The output reflection coefficient (with Vg=0) can be expressed in terms of the generator
impedance Zg and the S-parameters as
where is given by
The input reflection coefficient obtained for a microwave transistor with ZL = Zo is
The voltage standing wave ratios for the input and output ports are
| |
| |
| |
| |
Scattering transfer parameters (ST-parameters) is related to the incident and reflected waves as
[ ] [ ] [ ]
It can be shown that

4. Two port network with LTspice
Using .net LTspice command can find two port parameters such as Z, Y, H and S parameters.
The input impedance and the output impedance can also be found.
An example is giving below.
Fig. 1. Circuit example from [2]
Use the function .net I (R1) V1 to be able to plot the two port parameters and run the
simulation to plot the parameters by using PlotSettings/AddTrace (or CTRL-A in the Plot menu)
[2].

5. Fig. 2. The plot window.
Fig. 3. The magnitude frequency responses of the S-parameter for the circuit.
Fig. 4. The phase frequency responses of the S-parameter for the circuit.
As can be seen from the plots, the network is reciprocal (S12 = S21) and symmetrical (S11 = S22).

6. Reference
[1] M. Sadiku, Elements of Electromagnetics, 5th
ed., Oxford, 2011.
[2] Two port parameters with LTspice, JB de Swardt -October 2014, Available:
http://courses.ee.sun.ac.za/HFTegniek_414/JB/notas/Two%20port%20parameters%20in%20LT
SPICE.pdf
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