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Measuring RF impedance by the three voltmeter method

There is a range of methods of measuring impedance, and today some using very sophisticated techniques come within the budget of hams. For some reason, the availability of these instruments has stunted thinking in applying simple techniques to the impedance measurement problem, and those whose budget does not extend to the latest technology cry that they are disadvantaged.

Well, the new technology wasn't there is the past, yet we made do with simpler, even if less convenient and less accurate methods.

Method

An old technique for measuring RF impedance which uses a very inexpensive test box was to insert a known resistor between a steady source and load, and to measure the magnitude of the RF voltage across the three elements:

Since these three voltages appear in a loop, by Kirchoff's Voltage Law, the sum of these voltages having regard to their magnitude and phase is zero. If we measure the magnitudes of each of the three voltages, we have sufficient information to calculate their phase relationships, and from that, the unknown load impedance can be calculated.

Fig 1: Phasor diagram

 

Above is a phasor diagram of the voltages V1, V2 and V3 as a result of a complex load with series equivalent voltages of VR and VX.

The cosine of angle θ can be calculated from V1, V2, and V3, but θ can have a positive or negative value, meaning X may be capacitive or inductive. Since the same current flows through Rx as Rr, Rx=V3/V2*Rr*Cos(θ) and Xx=V3/V2*Rr*(1-Cos(θ)^2)^0.5. The solution of these triangles is a bit tedious, a calculator is provided below.

In the example in Fig 1, when the source is adjusted so that V1 is 10V, V2 is 4.789V and V3 is 5.747V. This gives Rx=48Ω and Xx=36Ω.

Fig 2 Example measurement box

 

Above is a circuit of a test box, the RF source is connected at the left, and the unknown load at the right. R1 is critical, it needs to be a known value non-inductive resistor and capable of dissipating a couple of watts (eg two 100Ω carbon film 1W resistors in parallel is fine for HF).

If the input voltage is 10-15Vpk, the response of the detectors in the range of interest if fairly linear. At higher voltages, the diodes may be damaged, at less than 5Vpk in, linearity and accuracy are compromised significantly.

The detector circuits provide three DC voltages V1, V2, V3 proportional to the magnitude of the RF voltage across the three elements and which can be measured with a DMM.

Fig 2: Detector from VK5JST analyser

Fig 2 above is the detector circuit extracted from the VK5JST analyser. It is an equally good alternative. The reason an RFC is used in Fig 1 is that it balances the three channels a little better, but the accuracy improvement is trivial compared to the accuracy of the instrument overall.

Calculator

This calculator solves takes the three measured voltages and calculates Rx and |Xx|. The sign of Xx is not given by this method, and needs to be found by some auxiliary test (like inferring it from change in |Xx| with change in frequency). BTW, plenty of low end impedance measurement instruments have this limitation, eg the prolific MFJ-259B.

Inputs:
V1 (V)
V2 (V)
V3 (V)
Rr (Ω)
Zo (Ω)
 
Results:
R (Ω)
|X| (Ω)
VSWR

SVN:

The calculator does not do a lot of error checking, if you enter nonsense, it will produce nonsense. VSWR is calculated wrt Rr. If V1>V2+V3 it is a measurement error, no results can be calculated. NaN means Not a Number, check the input values.

Table 1: Input field descriptions
Input field Meaning
V1-3 The voltages read with a high impedance voltmeter (preferably DMM)
Rr The reference resistor from the circuit used.
Zo  Impedance for calculation of VSWR

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Changes

Version Date Description
1.01 03/06/2011 Initial.
1.02    
1.03    
1.04    
1.05    

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