Mixing with Deformed Local Oscillator Signal

Question

I've decided to build up an AM receiver which is intended to capture sound signals from a nearby broadcasting station that is operating at 954 kHz. I've completed the system design and started to test one of the first segments of the receiver which is downconverting the arrived signal of concern into the IF frequency of 455 kHz.

For that conversion, I've utilised a mixer that will use a local oscillator that is based on a PWM signal generator: The PWM signal has a duty cycle of 0.5 and frequency of approximately 470 kHz. That signal is directed into a band-pass filter that has the lower and upper corner frequencies of 1.1 MHz and 1.5 MHz respectively so that the sinusoidal component of approximately 1.4 MHz that is inside that square wave can be obtained and used for downconversion. The relevant sinusoidal frequency component can be seen in the following figure which is the Fourier transform of the PWM signal (Useful info about the frequency component is highlighted with blue colour in the table.).

Of course, that sinusoidal signal is then amplified to a sufficient level for the sake of operation.

I've chosen LM318N for the system and the diagram of the test circuit on Multisim is given below:

And the output signal is as follows:

Obviously, the LO signal is not a pure sine and has deformed amplitude envelope. Could that waveform cause the whole receiver system to fail if it is implemented on real life?

Answer 1

It looks like that signal is doing a pretty good job of passing the correct signal, but it's leaving in some of the fundamental at 470kHz. You probably only have a suppression ratio of 20dB or so, which isn't good, but it isn't hopeless. The critical thing that I see in that is that you can draw a line through it, and the desired signal consistently goes above and below the line.

Thus, it depends heavily on the mixer you use, but that should probably work. It won't win any prizes for best radio ever, but if your goal is just to get something working -- go on to the next step!

I suggest that if you're doing this as a learning exercise, that you build your radio in blocks, so that you can swap out one block for another. Get it working with this LO, then if you want to improve it you can build another, better LO and try that, instead of having to build a whole new radio.

(And note: generating a square wave and then filtering it for an LO is a perfectly acceptable way to proceed -- it just looks like you need better filtering. So you can do that later, after you get the rest of the radio working).

Answer 2

First of all: yes, oscillator imperfections are one of the systemic sources of noise, self-interference, unintended interference from others, and general annoyance in receivers.

What you should do to figure out whether this is a problem here is start by realizing what a mixer does: It takes your LO signal and the RF bandpass signal and multiplies them.

The convolution theorem of the Fourier transform tells us that multiplication (in time domain) is equivalent to a convolution of the two in frequency domain. Now, the ideal LO, in frequency domain, has only two discrete frequency components: one at the positive LO frequency $+f_{LO}$, one at $-f_{LO}$, so the signal is $S_{LO}(f) = C(\delta(f-f_{LO})+\delta(f+f_{LO}))$, for some constant $C$ encapsulating amplitude and phase of the LO).

Now, convolving with a $\delta$ is –conveniently– simply shifting. So, your mixer shifts in frequency domain. Nice! Once

• by $-f_{LO}$ (mixing $f_{RF}$ to $f_{RF}-f_{LO}$, so closer to 0 Hz, and $-f_{RF}$ to $-f_{RF}-f_{LO}$, so further away from 0 Hz), and
• once by $+f_{LO}$ (mixing $f_{RF}$ to $f_{RF}+f_{LO}$, so further away from 0 Hz) and $-f_{RF}$ to $-f_{RF}+f_{LO}$, so closer to 0 Hz).

And which you get can be selected using simple real-valued low- or highpass filters.

Now, your LO is not just a perfect single harmonic, but still looks somewhat periodic. I'd wager a guess that you might describe it as cosine, modulated by some beat frequency, so that in frequency domain, you get the sum of two different sets of $\delta$ with different amplitudes, phases and frequencies.

So: What happens here is that you get various frequency components at $\pm f_{RF} \pm f_{LO,1}\pm f_{LO,2}$. This becomes a problem when bandwidth of the RF bandpass signal is large enough so that these overlap – and then you get self-interference.

Whether or not that is the case for you here – we can't tell you! But it becomes easy once you sit down, make a drawing of your signal (and their bandwidth) in frequency domain, and sketch where the modulation products end up. (if you need an example of what such diagrams might look like, this or anything that has "frequency" on the horizontal, and "power density" on the vertical axis).