Antennas and Microwaves

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Matlab RFutilities

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Time Domain Reflectometry

Normally TDR involves sending a very short impulse (voltage spike) down a transmission line, any discontinuities on the line will reflect some or all of the impulse. The sign and amplitude of the returned signal can be used to determine the nature of the discontinuity e.g. Capacitive, inductive, impedance step etc.  The time taken for the signal to return identifies the position of the discontinuity, a bit like Radar for transmission lines.

As its name suggests all this occurs in the time domain. However it is also possible to make measurements in the frequency domain and use a Fourier Transform to convert the results to the time domain. This has the obvious advantage that you don’t have to buy another piece of test kit. A possibility that has not been lost on manufacturers of Vector Network Analysers (VNAs) , many have the necessary software built in.  

Another advantage of using a VNA is that the frequency domain data is in the form of  S-parameters. Characterising a balanced transmission line as opposed to an unbalanced one simply involves measuring 4-ports instead of 2. By combining the standard 4-port measurements to give mixed-mode S-parameters, different excitation and response characteristics for the line can be derived.

E.g. For a balanced line such as the one modelled in Sonnet, below.

Sd1d1 = (S11-S13-S31+S33) /  2

The lower case ‘d’ denotes differential.  So Sd1d1 represents the differential reflection coefficient for port 1 of the differential line, driven differentially.

Sc1c1 = (S11+S13+S31+S33) /  2

The lower case ‘c’ denotes common.  So Sc1c1 represents the common mode reflection coefficient for port 1 of the differential line, driven in common mode.

These mixed-mode parameters, with a little care and thought, can be displayed pretty much like standard S-parameters, and can be used for TDR. In the example below, a balanced stripline has been modelled in Sonnet Lite and characterised for 4-port S-parameters. The S-parameters were converted to mixed-mode equivalents and Sd1d1  used for TDR. The resulting plot clearly identifies the impedance step on the line, the values obtained were in good agreement with values for individual line sections (ref SONNET TIP below).  

There is a  really good practical paper on mixed-mode S-parameters titled :

‘Mixed-Mode S-parameters Characterisation of Differential Structures’ by

W.Fan, A.C.W.Lu, L.L. Wai and B.K. Lok   Link

The cautionary note advised by this paper is that the Sd(n)c(n) / Sc(n)d(n) family of parameters that represent the cross mode coupling I.e. Common-mode response to differential excitation and visa versa showed slight differences to results obtained from a 4-port VNA, capable of physically exciting common mode and differential modes.

The TDR display for the 2-section stripline model. The physical length of  each section of line was 100mm (200mm total).

Note that although Sonnet uses 50 Ohm port impedances for the S-param characterisation, the characteristic impedance for the differential structure is 100 Ohm. A 100mm  section of 100 Ohm line was inserted at the input to the test line to avoid placing a discontinuity at the point where the impulse would occur in the time domain. Thus the reference plane for the test piece is at 100mm             (graphs produced using the ‘data07.son’  data in example 11)

A balanced stripline modelled using Sonnet Lite. An impedance step was introduced by changing the line separation at the mid point.

SONNET TIP :

For lines without discontinuities, Sonnet will report Zo in the ‘Response Log’.

By defining the input ports to the lines as P(1) and P(-1), the response data for P(1) will represent the differential impedance.

Defining  both input ports as  P(1), the response data for P(1) will represent the common mode impedance.