Video: Tutorial on IQ Signals and IQ modulation/demodulation

[w2aew]

This topic has been requested many times, so hopefully this overview and tutorial helps to shed a little light on the subject:

[Bukurat]

Very interesting.

[IanB]

OK, I watched the whole video, and there were two things I didn't follow:

1. When you add two sine waves of the same frequency, the resulting output wave has the same frequency as the inputs. Therefore, how can you modulate the frequency of the output without changing the frequency of the inputs?

2. How were you able to multiply a sine wave by a discrete 1/-1 signal using a mixer?

As someone unfamiliar with the field, I was unable to fill in those gaps using existing or prior knowledge.

[w2aew]

OK, I watched the whole video, and there were two things I didn't follow:

1. When you add two sine waves of the same frequency, the resulting output wave has the same frequency as the inputs. Therefore, how can you modulate the frequency of the output without changing the frequency of the inputs?

Frequency deviation is accomplished by sinusoidal variation of I and Q, effectively rotating the vector in the phasor diagram, similar to the second hand on an analog clock. Frequency shift is equal to the rotational speed of the I/Q vector. Another way to think about this... Continuous sinusoidal variation of I and Q results in the sum's phase being shifted by some delta amount for each carrier cycle.

2. How were you able to multiply a sine wave by a discrete 1/-1 signal using a mixer?

As someone unfamiliar with the field, I was unable to fill in those gaps using existing or prior knowledge.

The mixer is a balanced modulator, thus can multiply by positive and negative values. Check out my video on the diode ring mixer for some of the basics. Similar thing at play here.

[Skimask]

How would you keep the TX and RX L/O's synchronized?  Or, at the exact same frequency?
Seems to me if one drifted off the other by more than 1/2 of the smallest phase shift possible/used, everything would get out of sync and useless...

[w2aew]

How would you keep the TX and RX L/O's synchronized?  Or, at the exact same frequency?
Seems to me if one drifted off the other by more than 1/2 of the smallest phase shift possible/used, everything would get out of sync and useless...

Small frequency differences can (and is) easily be taken into account in the IQ processing in the receiver. 

[Skimask]

Small frequency differences can (and is) easily be taken into account in the IQ processing in the receiver.

Yes, makes sense.  (Forgot the topic was kinda heading more towards software SDR rather than hardware only solutions)

[coppice]

How would you keep the TX and RX L/O's synchronized?  Or, at the exact same frequency?
Seems to me if one drifted off the other by more than 1/2 of the smallest phase shift possible/used, everything would get out of sync and useless...

In the general case you don't want the LOs to be at the same frequency. As soon as one of the parties moves, Doppler means the frequency of the received signal is no longer the same as the LO at the transmitter. If the maximum frequency offset is guaranteed to be small, and the signal is differentially encoded, a simple modulation like QPSK might let you get away without doing a proper received carrier recovery -  although the differential encoding doubles the bit error rate. Pretty much anything more advanced demands a proper recovery of both the frequency and phase of the carrier at the receive end.

[IanB]

OK, I watched the whole video, and there were two things I didn't follow:

1. When you add two sine waves of the same frequency, the resulting output wave has the same frequency as the inputs. Therefore, how can you modulate the frequency of the output without changing the frequency of the inputs?

Frequency deviation is accomplished by sinusoidal variation of I and Q, effectively rotating the vector in the phasor diagram, similar to the second hand on an analog clock. Frequency shift is equal to the rotational speed of the I/Q vector. Another way to think about this... Continuous sinusoidal variation of I and Q results in the sum's phase being shifted by some delta amount for each carrier cycle.

Ah, I see. I did an experiment to see how this works out (see illustration below). And then I realized this follows immediately from trigonometry 

[coppice]

I think a lot of people will look at this video and immediately see that something is amiss with the waveforms - i.e. the kinks. I know this is an introductory video, but I think some brief mention of the need for bandwidth control in practical QPSK modulation would have helped the astute observer realise the presentation is not bogus.

[w2aew]

I think a lot of people will look at this video and immediately see that something is amiss with the waveforms - i.e. the kinks. I know this is an introductory video, but I think some brief mention of the need for bandwidth control in practical QPSK modulation would have helped the astute observer realise the presentation is not bogus.

I purposely made the phase transitions very fast so that they are obvious to see.  If they were filtered as they would be in the real application, the phase change wouldn't be so obvious.  I did make a text annotation in the video that talks about this.  I'm assuming that the viewer is savvy enough to understand that these baseband signals would be filtered in the "real world".

[coppice]

I think a lot of people will look at this video and immediately see that something is amiss with the waveforms - i.e. the kinks. I know this is an introductory video, but I think some brief mention of the need for bandwidth control in practical QPSK modulation would have helped the astute observer realise the presentation is not bogus.

I purposely made the phase transitions very fast so that they are obvious to see.  If they were filtered as they would be in the real application, the phase change wouldn't be so obvious.  I did make a text annotation in the video that talks about this.  I'm assuming that the viewer is savvy enough to understand that these baseband signals would be filtered in the "real world".

Many people go through entire digital comms courses and still fail to grasp the idea of excess bandwidth. In fact, a lot of well know digital comms books try to avoid the issue entirely, and only cover things like TED algorithms that could never work with real world amounts of excess bandwidth.

[MattSR]

Thank you for the video w2aew. Complex numbers can be tricky to grasp but they are essential building blocks in signal processing.