The applet examines the performance of a 90° 3-dB coupler-based multiplier using two square-law detector diodes (D1 and D2) on the coupled ports.
The input signal voltage amplitude ratio, the coupler Coupling factor (0.7071 for a 3-dB coupler), coupled line loss, and all port component impedances are adjustable with the scrollbars.
The main display plots the multiplier equivalent vector output voltage (blue) and the equivalent vector phase error (magenta).
To demonstrate the range of plot errors, the input phase is cycled through 360° at a rate such that the error limits are conveniently observable. At any signal frequency, any phase error between curves bounding the maximum and minimum are possible.
At the top of the display, the data list reports the cursor frequency as a ratio of the coupler center frequency, the relative output amplitude, and the phase error.
The input phase difference is also listed so that the phase error at that point is identified.
The phase error is derived by simulating a second multiplier having a perfect 90° phase-shifter in series with one input. In practice this may be implemented using a third 90° coupler that could also add a phase error offset to the plots; the phase offset is obtained from the directional coupler applet of Chapter 3.

User Notes:
An ideal multiplier based on a 90° 3-dB coupler, with inputs A cos(ω t) and B cos(ω t + φ) produces an output proportional to AB sin(φ); one component of a vector amplitude AB and phase φ.
In practice, there are amplitude weighting errors varying with frequency (coupler amplitude response) and phase errors (coupler amplitude and phase response).
This applet shows that for a practical microwave circuit, output vector phase errors increase with input signal unbalance and degraded port VSWR.
The useful frequency range (amplitude flatness) also reduces.
Whilst maintaining correct diode match is important, mismatch appears to be tolerated providing the two diodes remain a matched pair.
Maintaining near equal input amplitude balance appears essential for wide band operation.
Slight overcoupling improves the practical operating bandwidth.