# AM receiver - utilising bandpass undersampling and quadrature mixing

Started by July 27, 2006
```Hi,

I am new to the whole DSP thing (very new) and have a question regarding
the use of undersampling and quadrature mixing to demodulate a signal in a
given range.

I have been trying to research the topic but have not been getting very
far. I understand how the bandpass signal can be undersampled at a rate of
2B without aliasing if the proper bandedge frequencies or chosen but have
no real idea what the quadrature mixing is about??

From what I've read it phase shifts the signal 90 degrees to allow 2 ADC's
to operate in tandum at half the sampling rate. Is this correct? Is it half
of the 2B sampling rate? A quadrature mixer converts the received AM signal
to the I and Q component signals representative of the AM signal, and a
signal filter passes a desired frequency segment of the I and Q component
signals.

So a bandpass filter is used initially to take the intermediate bandwidth
required. This is then fed into a quadrature mixer sampling at a rate of
2*the IF BW. This mixer has two ADC's which sample at the rate of BW. The
sampled data from these ADC's can be taken and the amplitude of the
original sample determined using mathematics because they are exactly 90
deg out of phase. From here the amplitude is put back into a DAC sampling
at 2*B to demodulate the signal.

Is this correct or sort of correct? What other filters are required in the
setup. I imagine my explanation is very simplistic and skips over a fair
bit of stuff. How does a quadrature mixer work? I have read that it needs
a locat oscillator - what should the oscillaro frequency be set at?

Can somebody point me to some specific information on the topic. I really
need a simple block diagram illustrating the components in the system but
have been unable to find one. How would a reciever use bandpass
undersampling and a quadrature mixer to demodulate an AM signal?

Thanks
Thedspkid - thedspkid@gmail.com

```
```thedspkid wrote:

> Hi,
>
> I am new to the whole DSP thing (very new) and have a question regarding
> the use of undersampling and quadrature mixing to demodulate a signal in a
> given range.
>
> I have been trying to research the topic but have not been getting very
> far. I understand how the bandpass signal can be undersampled at a rate of
> 2B without aliasing if the proper bandedge frequencies or chosen but have
> no real idea what the quadrature mixing is about??
>
> From what I've read it phase shifts the signal 90 degrees to allow 2 ADC's
> to operate in tandum at half the sampling rate. Is this correct?

Yes.

> Is it half of the 2B sampling rate?

Yes, sorta.  I'll answer in two parts:

The "Yes" part:

The Nyquist criterion says that you have to sample at least 2B, but it
doesn't say they have to be evenly spaced in time.  If you can find two
unique ways to sample you can sample the pair at 1B.  This can be I and
Q signals, or it could be the signal and it's derivative, or anything
else that gives you two unique views of the signal.  In theory you could
sample on 100 parallel channels at B/50, but in reality you wouldn't
find 100 different aspects of the signal that you could _reliably_ sample.

The "sorta" part:

The Nyquist criterion is for a strictly band limited signal.  'B' in
this case is the bandwidth beyond which there is _no_ signal energy.  In
practice there is no such thing as a perfect filter that completely
blocks all signal content above some magic frequency.  Mathematically,
if such a filter _could_ exist it would take an infinite amount of time
to settle.  So in reality you have to understand how sampling a signal
aliases it, and use a sampling rate that reduces your unwanted signal.

> A quadrature mixer converts the received AM signal
> to the I and Q component signals representative of the AM signal, and a
> signal filter passes a desired frequency segment of the I and Q component
> signals.

Correct.  Actually a pair of signal filters.
>
> So a bandpass filter is used initially to take the intermediate bandwidth
> required. This is then fed into a quadrature mixer sampling at a rate of
> 2*the IF BW.

Well over 2*BW, unless 'BW' is the 60dB attenuation frequency or something.

> This mixer has two ADC's which sample at the rate of BW. The
> sampled data from these ADC's can be taken and the amplitude of the
> original sample determined using mathematics because they are exactly 90
> deg out of phase. From here the amplitude is put back into a DAC sampling
> at 2*B to demodulate the signal.

Correct.  Or of there's more to the 'demodulation' than just playing the
music the baseband signal is further processed.
>
> Is this correct or sort of correct? What other filters are required in the
> setup.

For AM voice and music, just a reconstruction filter off of the DAC.
This can be pretty simple if you do interpolation in the digital domain
and oversample on the output.

> I imagine my explanation is very simplistic and skips over a fair
> bit of stuff.

It's actually not too bad.

> How does a quadrature mixer work? I have read that it needs
> a locat oscillator - what should the oscillaro frequency be set at?

Nearly all radio receivers these days are superheterodyne designs, which
means they have local oscillators and mixers.  A quadrature mixer just
uses two parallel mixer channels and some way of deriving a pair of
local oscillator signals that are separated by 90 degrees.  This can be
done with an analog phase shifter, or you can generate the LO signal at
2x or 4x your desired receive frequency and divide it down, or you can
use any other clever way of getting a quadrature LO signal.
>
> Can somebody point me to some specific information on the topic. I really
> need a simple block diagram illustrating the components in the system but
> have been unable to find one. How would a reciever use bandpass
> undersampling and a quadrature mixer to demodulate an AM signal?
>
Get yourself a copy of the ARRL Handbook, published by the Amateur Radio
Relay League (of the US).  It'll go into a bunch of radio basics, and by
now it should have this whole receiver described.  Don't let the
'Amateur' put you off -- most professional radio engineers have a copy
or two sitting at their desks because it's such a good practical reference.

If you're not in the US you may have better access to the RSGB (Radio
Society of Great Britain) handbook -- I believe it covers the same
stuff, but I can't vouch for it.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

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"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
```