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Re: [Discuss-gnuradio] why quadrature samples?

From: Johnathan Corgan
Subject: Re: [Discuss-gnuradio] why quadrature samples?
Date: Wed, 22 Jan 2003 18:08:42 -0800
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Matt Ettus wrote:

Thus you have sampled a BW of 2X by using 2 samplers of rate 2x, instead of
using one at a rate of 4X.

That was probably the most succinct, easy to follow explanation of "quadrature downconversion" I've ever seen :-) Google has numerous hits on the above term, but none of the explanations reduce it to the minimum essentials the way you have, so a non-"complex math geek" like myself can understand. (I'm a different sort of geek.)

An interesting variation on this is the "Tayloe Detector.", from Dan Tayloe, N7VE. It uses a quad CMOS switch and some capacitors to sample-and-hold the signal at 4x the center frequency of the bandpass of interest. Each switch then samples the signal at the center frequency, but at successivly 90 degrees phase offset from the previous switch. By using an opamp to "subtract" the 0 degrees and 180 degrees outputs (just apply them to the + and - inputs as is, with appropriate feedback), and a second opamp to do the same with the 90 degrees and 270 degrees outputs, you've just downconverted to baseband and have your I and Q outputs. A low-pass filter on these and you're ready for your soundcard (or just rely on the soundcard anti-alias filter instead).

Why is this good?

First of all, you can do downconversion very, very early (almost right at the antenna). Second, your "local oscillator" is really a digital squarewave, frequency doubler, and a 90 phase shifter. Thirdly, the conversion loss of the CMOS switch is much less than say, a double-balanced mixer. Finally, using a high-speed, low-propagation delay, digital bus multiplexing chip as an RF "mixer" is a _way_ cool hack :-)

The performance of this kind of detector is limited by the phase noise of the LO and how closely matched the components are in each leg of the circuit.

Here is a good diagram of an actual implementation:


You can do fun and interesting (and baffling) things with I and Q to recover just about any form of modulation on the original signal. This would fall under the "narrowband" version of software defined radio.

-Johnathan, AE6HO

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