Scattering parameters (Sparameters) represent the way voltage waves propagate through an electrical network. High frequency linear networks can be fully characterised by these parameters which are measured at the ports of the network. Sparameters are a particularly useful measurement tool as there is no need to identify the components in the network to characterise it.
TwoPort Network Theory
Twoport networks are often used to describe how Sparameters are calculated, although Sparameters can be used to characterise electrical networks with any number of ports. The theory remains the same for different numbers of ports, only the number of parameters change. There are always N^{2} Sparameters for an Nport network, each one representing a potential inputoutput path. Sparameters are complex numbers. In a two port network there are four Sparameters.
In linear networks, when a voltage wave is incident on a port, the energy splits up:
 some energy goes into the port and exists
 some energy goes into the port and scatters to the other ports
 some energy goes into the port and is reflected back out
Sparameters represent the voltage ratios in the network and are are usually displayed in a matrix format. The first and second subscript numbers in an Sparameter for a twoport network is the output port number and the input port number respectively. The relationship between the incident voltage waves and the reflected waves is given by equation:
(1)
Where the variables are described as:
 a_{1  }voltage wave incident on port 1
 a_{2 }voltage wave incident on port 2
 b_{1  }voltage wave reflected from port 1
 b_{2  }voltage wave reflected from port 2
 S_{11}  input reflection coefficient
 S_{12}  reverse voltage gain
 S_{21}  forward voltage gain
 S_{22}  output reflection coefficient
Measuring Sparameters
Sparameters are typically measured using a voltage source and a matched load Z_{0} (load with the same value as system impedance). Sparameters are measured by successively opening and shorting different input/output ports of the network. The matrix in the equation above can be expanded to give the two equations:
(2)
These equations can then be rearranged for each Sparameter and using the maximum power transfer theorem (inserting a matched load at a port sets that ports voltage to zero), the equations for the parameters can be calculated using the following equations:
(3)
So for example, to calculate the input reflection coefficient of port 1 (S_{11}), the user would apply a voltage across the port 1, place a matched load at (or ground) a_{2}, then measure the voltage across b_{1 }and a_{1}. Dividing b_{1} by a_{1} gives the input reflection coefficient at port 1.
Example
The following example demonstrates how to extract the Sparameters from a twoport SAW in OnScale.
This SAW model has two ports each made up of two finger pairs.
To calculate the model's Sparameters, two simulations must be run to acquire all of the information to solve the set of equations (3):
 one that drives port 1 and grounds port 2 (saw_p1.flxinp)
 one that drives port 2 and grounds port 1 (saw_p2.flxinp)
 Open the post processing tool
 Load in both time histories (saw_p1.flxhst and saw_p2.flxhst)
 Select pize idt1_act:Voltage in the results manager
 Select the Sparameters button in the Home tab of the ribbon

Assign time histories to the appropriate records as follows:
 Select Calculate
 The results will appear in the results manager under the Frequency History section
 Sparameters can be plot by double clicking on the frequency history:
0 comments
Please sign in to leave a comment.