I’ve been receiving a few questions from the readers. (Yes, I actually have readers—other than you.)

## 2008-12-28 Update

I misread the email; the initial version of the I/Q noise figure discussion was completely wrong.

## I/Q Noise Figure

What’s the difference of noise figure between quadrature [downconverter] and single downconverter? In the quadrature downconverter, you have I and Q path, if required Nf=10dB for this quadrature downconverter, what’s the Nf for the path of I or Q? Can I see the Nf for RF to I path is 7dB, the same thing for Q?

— K. C.

Unfortunately, the answer is no. The important thing to remember when computing things in dB (and summing them) is whether they add in-phase (constructively) or not. Since the I and Q signals are completely orthogonal, if a 10 dB NF is required for the quadrature downconverter (I + jQ), then 10 dB is required for the each of the I and Q paths.

If, however, we had two paths that summed constructively, and we needed a 10 dB overall noise figure, then yes, each path would only need to deliver 10 dB (per path). Unfortunately, I and Q don’t do this constructive summation.

— H. M.

Unfortunately, the answer is no. Or sort of. Sure, I can elaborate, but I can’t do a very good step-by-step job because I don’t have access to Cadence ADE. So, I’m running on my own memory, which (as my friends know) is very dangerous.

However, here’s a rough step-by-step:

1. Break the loop by inserting an Iprobe element. (Usually, I choose an Iprobe). You usually want to break the loop in a point that’s high-impedance. Typically, I choose the highest impedance output node (transconductor) looking into a compensation capacitor. So, the Iprobe would measure current going from the transconductor into its compensation capacitor.
2. Start ADE (Tools –> Analog Environment). If it’s not already set in the ADE window, select Setup (?) –> Simulator/Directory/Host and select spectre.
3. Select Setup –> Analysis and select stb (stability). You’ll need to select start and stop frequencies. There’s also a button to select the loop gain element (Iprobe) that you’re using to break the loop. (You can have multiple Iprobes in a single schematic, for each loop you want to analyze.)
4. After you run it, you can choose Outputs –> Plot –> Loop Gain (?) or something like that to see amplitude and phase vs frequency. You can also choose the loopgain result from the results browser and do a direct phaseMargin() measurement on it, which will pick the phase margin. (Something like phaseMargin(-getData(‘loopgain’ ?result ‘stb’)) – but I’m typing from memory.)
5. Keep in mind that Cadence returns the exact loop gain, which is (or should be) 180 degrees at dc. However, the phaseMargin() function expects the loop gain to be 0 degrees at dc and then go to 180 (unstable) at some point later. So, you have to invert the result when using phaseMargin().

The stability analysis, I believe, uses the Middlebrook method,which really runs two ac analyses and combines the results to produce the return ratio. Most other circuit simulators (HSPICE RF) have a similar capability. If your simulator doesn’t, it is possible to get the equivalent by manually running the two analyses.

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