MPSKIQ and Direct Conversion TRX using an IQ-Modulator

The MPSKIQ program can be used for a simple direct conversion TRX design. The necessary Hilbert Transformation is already installed on the DSP and can be activated. When activated, both the IN & OUT stereo channels act as an IN & OUT for the complex de-modulation signals. The program delivers the necessary 90 degrees out of phase AF signals for an IQ-UP converter. When receiving, the AF-output of an IQ-DOWN converter can be fed directly into the stereo AF-input of the EZKIT. MPSKIQ is able to decode the complex IQ input and can easily be changed between upper and lower sidebands. In addition to demodulating the MPSK, MPSKIQ can also demodulate USB and LSB telephony.

The following graphic shows the principal connections to the EZKIT:

Some insights into IQ-mixers

To understand the mystic IQ-mixer, lets think about the well known real signal mixer which everybody will probably know, and forms part of most or the simple direct conversion RX designs.

Remember, when mixing (multiplying) two sinus signals e.g. an RF signal from the antenna f1=1001kHz with a local oscillator LO of f2=1000kHz, the result is the difference and the sum of these frequencies. This means that at the output of the mixer, we will find two frequencies at f3=1001kHz-1000kHz=1kHz and f4=1001kHz+1000kHz=2001kHz. The mixing product of f4=2001kHz can easily be removed by a simple low pass filter. After filtering the result is an AF of 1kHz. If f1 is a keyed CW signal, the AF f3 at the output will also be a keyed AF at 1kHz.

Up to now all is OK, but what happens when there is another RF signal from the antenna at 999kHz?
Lets think about it. We again get the difference and sum i.e. f3=999kHz-1000kHz= minus 1kHz and f4=999kHz+1000 kHz=1999kHz.
Yeah, the 1999kHz is no problem, but what's with the stupid minus 1kHz?
Negative frequencies, what's this?

Nothing special, you will also hear a 1kHz AF at the output of the simple real mixer, which  cannot produce the minus 1 kHz. It also delivers an AF at 1kHz, which overlays the AF resulting from the RF at 1001kHz

Signals lying up or down the same distance from the LO will result in the same AF frequency at the output.
Let's consider: we can not decide, if a received AF signal results from an RF lying below or above the mixing frequency. That's exactly the reason why the simple direct conversion receiver concept cannot decide between USB and LSB. It can demodulate DSB but when receiving USB or LSB, the resulting AF will be overlapped by noise resulting from RF lying on the opposite sideband.

How to overcome this nasty disadvantage. We need a mixer, which can decide whether we get positive or negative frequencies as a result of the mixing. The key to solving this problem is to understand the mystic negative frequencies.

Negative frequencies

A primitive direct conversion TRX consists of a local oscillator pair with two identical frequencies with a phase difference of 90°. That results in the possibility to decide whether the result of the mixing process is a negative or a positive frequency.

What is a negative frequency? To get an idea, lets have a look to the following graphics.

Imagine that the phasor is turning around with a specific speed or cycles per second. The projection (shadow) of the phasor to the real-axis will result in a sinoid time signal x(t). It should be obvious that the projection of a phasor running in clockwise or counter-clockwise direction should result in the same projection x(t), even if the phasor is running in positive or negative direction. The direction of the phasor gives the decision of whether it is a positive or negative frequency. Simple projection of the signal to the real axis gives us no information, what we need is an additional projection to the j-axis. The difference between positive and negative frequencies is the phase relationship between both components.

If the LO has f2=1000kHz and f1=1001kHz, the result after low pass filtering is the 1 kHz sinoids. With f2=1000kHz and f1=999kHz the result is the -1 kHz sinoids. With just one mixer, the decision can not be made whether there is 999kHz or 1001kHz, but after mixing the input with two frequencies at equal frequency, but 90° out of phase, we get two signal components, forming a so called complex time signal. The two components of the complex time signal are called Inphase and Quadratur. Inphase components result from mixing with a cosinus and Quadratur components from mixing with a sinus time signal of the same frequency, so giving this special mixer the name IQ-Mixer.

Now we are half way there. We have a complex time signal with a positive or negative frequency. Unfortunately we can not hear complex signals, only real signals. But the solution is very easy.

The inphase signal is processed by an all pass filter, which doesn't change the amplitude, but causes a phase shift of 90° degrees, independent of the input frequency. Such a filter is called a Hilbert Transformation. The ideal Hilbert Transformation like the ideal low pass is not realizable and only an approximation is possible. At low frequencies it's very difficult, which is easy to understand, because a delay of 90° phase shift at DC means an infinity long delay, which is not possible to arrange. So any physical implementation of such a filter is limited to a certain frequency range f>0. That is no problem, when the modulating signal has no DC, which is true for PSK and telephony. An analog solution for a Hilbert Transformation is possible, but the accuracy is limited due tolerances in the components. Much better is an implementation using a digital signal processing. The program MPSKIQ already contains the necessary filter functions.

The graphics shows, how to extract the positive or negative frequencies. By adding both components of the  signal after phase shifting, we cancel the positive frequencies, subtracting will cancel all negative frequencies. This is done just by changing the sign of the adder. So we can switch between reception of USB or LSB.

The same ideas are also valid for generating a SSB signal, just by changing the direction of the mixers. MPSKIQ already delivers the necessary 90° phase shifted audio signals.

May 1999, Michael Keller