RF resistive Brige Measuring bridgeResistive Bridge

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I am building an RF resistive measurement bridge. I want to be able to measure the impedance of an antenna over a wide power range. SWR meters are far too inaccurate for this purpose.

An RF resistive bridge consists of just two 50 Ω resistors. It has one input E and two outputs A and B.
RF is fed into input E, where a signal source TX with 50 Ω source impedance is connected. Port A is typically terminated with a reference load, e.g. a 50 Ω dummy load. Port B is connected to the unknown impedance.
Milling and drilling an aluminium block.
Two resistors of type RFR 50-250: 50 Ω, 250 W each. Each bridge resistor is loaded with approximately one quarter of the input power. Theoretically up to around 1000 W could be fed into input E; I work with a maximum of 100 W.
A dummy load is connected to each of ports A and B to verify the symmetry of the bridge.
Two oscilloscope probes are additionally connected to ports A and B. The probes are type P6100, inexpensive Chinese probes with approximately 10 MΩ and 20 pF input impedance. For a measurement at 1.8 MHz the capacitive reactance is about 4.4 kΩ, which has negligible loading effect on the 50 Ω bridge.
Measurement is done with a Digilent AD3. Together with the 1:10 probes, up to 250 V_p can be measured, which is more than sufficient. The power at input E is adjustable: 5 to 100 W from the transmitter, a fixed 30 dB attenuator, and a variable 0 to 31 dB attenuator in 1 dB steps. This gives a range from 100 W down to 4 µW (+50 dBm to −24 dBm) in 1 dB steps.

AD3 waveforms: sampling at 100 MHz, 5 V/div, 25 V_p maximum. I compute the FFT and extract the amplitude at the signal frequency. The amplitude can be determined very precisely, down to the millivolt range.

Theory: Antenna Impedance from Bridge Voltages

The resistive bridge is driven by a source E with 50 Ω internal impedance. The two bridge resistors are each 50 Ω. Port A is terminated with a 50 Ω reference load; port B is connected to the unknown antenna impedance Z_A.

The bridge equations are:

A = E / 2 (A is the reference voltage at port A)
B = E · Z_A / (50 + Z_A) (B is the voltage at port B)

With E = 2A the antenna impedance follows directly:

Z_A = 50 · B / (2A − B)

In the general (complex) case, A is taken as the phase reference (phase = 0°), so A = a (real). Channel B is measured with amplitude b and phase difference φ, giving the complex voltage B = b · (cosφ + j sinφ). Substituting:

Z_A = 50 · b e^jφ / (2a − b e^jφ)

This yields both the resistive part R and the reactive part X of the antenna impedance Z_A = R + jX, which can be plotted directly on a Smith chart. The reflection coefficient and SWR are:

Γ = (B − A) / A SWR = (1 + |Γ|) / (1 − |Γ|)

If no phase measurement is available, only the RMS amplitudes a = |A| and b = |B| are known. In that case φ is unknown and only |Γ| can be determined:

|Γ| = |b − a| / a

This gives the SWR but not the full impedance Z_A.