Antennas and Microwaves

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Balanced Measurements

The Theory

There many instances in RF and antenna work where a balanced transmission line or radiating element is used. Creating a physical balun so that measurements can be made on a single ended system  is  one option. However, the physical realisation is seldom ideal over the frequency  range of interest and often just adds uncertainty to the results.

Another option is to calculate the balanced impedance from 2 single ended measurements.

The derivation of the balanced line impedance presented here takes an intuitive approach to the problem, see figure 1 below.  The unbalanced system is a standard 2-port network. Port 1 is fed by a generator (Ep) with source impedance Zo and port 2 is terminated in Zo. The balanced system is a 3-port network, ports 1 and 2 are fed differentially by generators (Ep/2) and (-Ep/2) respectively, port 3 is terminated in Zo.

The reflection coefficient, Rho is defined as the (return signal) / (incident signal). For the unbalanced system this is just S11. For the balanced system the reflection coefficient simplifies to (S11-S12) and (S22-S21) for ports 1 and 2 respectively. See figure1.

Having established the reflection coefficients Rho(bal1) and Rho(bal2) for each arm of the system, the input impedance is readily calculated  using Zin=((1+Rho)/(1-Rho))*Zo. The total balanced impedance is then just the sum of the two arms Zin1 and Zin2, giving the following result :

Replacing -Ep/2 in figure 1 with                   for the port 2 excitation yields a more generalised result :

Where (Theta) in radians represents the angle between the excitation phases.

Theta = pi     balanced feed

Theta = pi/2  quadrature fed

Theta  = pi     co-phased

Figure1

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Practical Measurement

In order to make practical use of this result the device under test (DUT) has to be characterised with a full set of s-parameters (S11,S12,S21,S22). These need to be post processed on a PC to give the balanced impedance. This can then be displayed directly or cascaded with other components to give an overall system response.

Note that the S-parameters must be corrected to the appropriate reference plane, this sounds obvious but Network Analysers can give you your S-parameters in numerous formats, with/without error correction and almost always without electrical delay included (see page 2).

To make the system as near 'real-time' as possible the Network Analyser can be controlled by the PC using a package like LabView or MATLAB allowing the post processing to be done using the same package. Using this approach balanced line impedance measurements can be made in a one keystroke operation.

Balanced Measurements

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