## Gunnplexers and I/Q Demodulation

My 10 GHz radar, based on a Gunnplexer type system, has a pair of detector diodes spaced some distance apart in the waveguide. This provides a way to separate positive and negative doppler returns by using the two detected signals as I and Q inputs to a FFT. Here's a schematic view of the top of the waveguide:

The two detector diodes are separated by 1/8 of a wavelength, which is electrically equivalent (because the two signals are so close in frequency) to the conventional I/Q demodulator as shown in the following two diagrams.

So, how does having I and Q help you distinguish between motion towards and away from the Gunnplexer? When you have both I and Q, you can distinguish positive and negative doppler frequencies, because the relative phases of the doppler signals are different.

Consider a target moving towards the Gunnplexer, with a velocity such that the return is shifted by a radian frequency of "doppler". The two signals are:

Vout = cos(omega * t)
Vin = cos((omega+doppler)*t)

The inphase mixer forms the product:

Imixer = cos(omega*t) * cos( (omega+doppler)*t)
= 1/2*cos( omega*t + (omega+doppler)*t) + 1/2*cos( omega*t - (omega+doppler)*t))

The quadrature mixer forms the product:

Qmixer = sin(omega*t) * cos( (omega+doppler)*t)
= 1/2*sin( omega*t + (omega+doppler)*t) + 1/2*sin( omega*t - (omega+doppler)*t))

ignoring the sum term (which is at 20 GHz, and doesn't make it very far) we get:

Imixer = 1/2*cos( (omega- omega+doppler)*t) = 1/2*cos(doppler*t)
Qmixer = 1/2 * sin( (omega- omega+doppler)*t) = 1/2*sin(doppler*t)

These are just a pair of sinusoids with the Qmixer signal 90 degrees lagging the Imixer signal (if doppler>0). If doppler is negative, Q will lead I. Sketch out the sinusoids and all will become clear.

And, for negative frequency, where the sin(-t) signal leads the cos(-t)

If you're building a burglar alarm, you can probably just clip or threshold the two signals and then use some simple logic gates to generate "going towards" pulses or "going away" pulses, much the same as a quadrature encoder. (Quad encoders actually work by just this principle).

If you're digitizing both signals, and feeding them into an FFT as real and imaginary components (which is what I do), then the peak will show up as negative or positive frequencies, as appropriate. Sometimes, you may have to fool with your FFT program, since many of them assume that the second half of the transform is just a mirror image of the input (which it is, if the input is real only), and don't display it.

You can see some sample data from real targets.