# How is the Hackrf able to achieve 20MHz of bandwidth with an ADC that only allows 22Msps?

The way I understand it, is that to avoid aliasing on an ADC, you have to be in the first Nyquist zone (so half the sampling speed). What doesn't make sense to me is how the Hackrf is able to bypass this, and achieve 20MHz of bandwidth, even though the 1st Nyquist zone would be only 11MHz.

I notice from the schematics that the MAX5864 ADC is two channels, with the baseband I signal going into one channel, and the baseband Q signal going into another. Do the two channels get added together, to form an overall bandwidth of 20MHz?

Also, while I'm at it, what exactly is the purpose of using in an sdr? Is it to make modulation/demodulation easier?

• Hello and welcome to ham.stackexchange.com! – rclocher3 Feb 22 at 16:07

Another way to look at it is that an IQ ADC is really taking 2 independent (not added together) samples per IQ sample. Thus the rate of information gathered is double from a just scalar sampling at 22 MHz. The 90 degree offset between the 2 IQ sample components allows capturing phase information that can help a complex FFT (et.al.) differentiate between what would have been aliasing between spectrum above and below the heterodyning LO frequency.

• Thank you! That makes sense – camerakid Feb 24 at 2:33

The Nyquist limit is half the sampling rate because otherwise you can't distinguish a signal at a frequency $$x$$ from a signal at $$f_s - x$$ which starts 180° out of phase from the first one — they give exactly the same sequence of real samples. But quadrature sampling gives exactly the phase information needed to resolve this ambiguity. Knowing $$\sin \omega t$$ limits us to two of four quadrants, but knowing $$\sin \omega t$$ and $$\cos \omega t$$ at the same time limits us to one quadrant. With this distinction provided, it's possible to distinguish frequencies up to $$f_s$$ — or a little less, given that we still need to filter out frequencies above the sample rate, and filters have skirts.

• Interesting, I did not know that. So (if I understand correctly): if you have an ADC with two channels at freq x, you can use both to sample (and reconstruct afterwards) an I Q signal up to (almost) frequency x? Correct? – Dieter Vansteenwegen ON4DD Feb 22 at 8:39
• @DieterVansteenwegenON4DD You can double the bandwith with two ADC channels, but only if they are fed with orthogonal, i.e., separated by 90° shift, phases. – OH2FXN Feb 23 at 18:18
• @OH2FXN Thanks, that makes sense! – Dieter Vansteenwegen ON4DD Feb 24 at 9:27
• "The Nyquist limit is half the sampling rate because otherwise you can't distinguish a signal at a frequency x from a signal at fs−x which starts 180° out of phase from the first one — they give exactly the same sequence of real samples" - is this really the reason for the Nyquist limit? I thought it had to do with not being able to distinguish higher frequencies (by higher I mean further from zero)? I thought the IQ sampling approach works because it turns the signal into 2 signals each having half the bandwidth, and each one is sampled at the usual Nyquist rate? – John B Feb 24 at 16:42
• @JohnB $f_s$ is the sampling rate (double the Nyquist rate), so $f_s - x$ is a higher frequency. :) You also get aliases at further multiples of $f_s$ but that doesn't come into play here. And yes, what you said is true, but it's not like I is USB and Q is LSB, and you put them together to get both sides of the carrier. The relationship really works like I said in my answer. – hobbs - KC2G Feb 24 at 19:09

Are the two channels added together? Yes and no.

The whole point of collecting I and Q is so they can be treated as real and imaginary parts of a single complex sample.

This is one of the key methods of SDR.