where N = noise density, volts/root Hz, fed to VCO tune port Kv = tuning slope, Hz/V fos = offset frequency, Hz
Two things -
How is this equation derived?
Assuming the op-amp noise density is flat, L(fos) falls with increasing fos - so it could never produce a plateau. Is a phase noise plateau around the carrier *always* a tell-tale sign of phase comparator and/or reference noise?
PS - The vital statistics of my PLL are:
Comparison frequency = 100 KHz Output frequency = 15.6 MHz (i.e. divider N=156)
-3dB Loop bandwidth ~ 300 Hz VCO (Mini-Circuits POS-25) tuning sensitivity = 2.58 MHz / Volt Reference oscillator = 10 MHz DIL-14 xtal module Phase detector = AD9901-style (XOR gate) The phase detector, reference and VCO dividers are implemented in an Altera EPM7128S CPLD.
After sleeping on it, a couple of things have dawned on me. Firstly, I can see the VCO gain k/s in that equation, but I still don't understand how/why it's possible to get dBc/Hz out from nV/sqrt(Hz) in, like this. Secondly, I've remembered the loop has a high-pass response to VCO noise, and a low pass response to noise injected *anywhere* else. So op-amp noise could make a plateau, right? The noise level I'm seeing just seems a bit high to be accounted for by the reference multiplied - but I don't know for sure.
In section 2.1 of "Digital PLL frequency synthesizers" Ulrich Rohde derives the amplitude of NBFM sidebands as thetaP/2 where thetaP = modulation index = deltaF / fmod where deltaF = max deviation and fmod = modulating freq.
If the peak noise voltage was N, the peak deviation would be deltaF = N*Kvco Relative sideband amplitude S(fos) = thetaP/2 = N*Kvco / fos / 2 So, I'm almost there, except for the root 2 thing - presumably something to do with peak/rms?
Without having looked at the equations much, my guess is that it's a consequence of power (which is what 'dBc' ultimately refers to) being proportional to voltage squared over a given impedance.
I'll confess I usually just rely on what the PFD manufacturers' simulations tell me when I need a prediction. I haven't tried homebrewing my own PFD chip (and don't intend to.)
I was sort of hoping one of the more qualified folks would chime in on your thread, as the question of exactly where your -70 dBc/Hz figure came from is an interesting one.
I agree; -70 dBc/Hz inband is not optimal for an HF PLL with a clean reference. How exactly are you measuring it? Are you using a spectrum analyzer whose synthesizer is noisier than your own? At HF, that's the rule rather than the exception, since most analyzers use multi-octave microwave LOs. I have seen people hook an 8563E up to an HP 10811 OCXO standard and conclude that its phase noise is -116 dBc/Hz at 10 kHz from the carrier. :)
Are you remembering to do the 10*log(RBW) thing to turn measured dB into dBc/Hz? If your equipment does this automatically, did you tell it to subtract the actual reference level (if not 0 dBm) before calculating dBc/Hz?
Noise from the opamp is really equivalent to noise internal to the VCO, if you think about it. A noisy opamp will usually affect the noise outside the loop bandwidth more than it will raise the height of the plateau. (Conceptually, where does the opamp's influence end and that of the VCO's tank circuit begin?)
The PFD can generate a correction signal to counteract noise contributions from both sources, but only within the loop bandwidth, and only down to the PFD's own noise-floor limit. The -70 dBc/Hz figure sounds to me like a measurement error, or a gross problem with the PFD implementation. None of the loop parameters you mentioned seem out of line to me.
Below the loop BW, the output phase noise will be determined by the reference, this includes the reference itself (which should be very clean in your case) and both the ref and var dividers and phase detector. The noise floor for dividers is about -140 dBc/Hz and is multiplied by N
Above the loop BW the phase noise will be the VCO and op amp (less whatever filtering there is after the op amp)
You can confirm your diagnosis by temporarily changing the loop BW and see what happens to the phase noise.
What is the phase noise for the VCO POS-25 alone at 200 Hz offset?
Since your loop BW is 300 Hz your output phase noise at 200 Hz can be only a little better than the POS-25 itself is. The phase noise of the VCO will be increasing as you go lower in frequency. But the loop gain will also be increasing as you go lower in frequency. These effects cancel giving you the plateau. Above the loop BW, the phase noise follows the VCO down. Going down , the plateau remains flat until the reference noise starts to rise and the output noise follows it up.
It'll definitely be interesting if you can post what happens with the smaller resistor value and quieter op-amp. My gut feel is that it won't make much difference to the noise inside the loop bandwidth, since the opamp and filter are inside the loop just like the VCO varactor is. But it sounds like you've already seen some results that suggest otherwise.
My current favorite PLL opamp is the LT1677. It is basically an OPA27 clone but it has true rail-to-rail capability and better CMRR/PSRR. Nice part when you need to drive a higher-voltage VCO.
Yeah, those are both neat apps. I like the idea of sending an analog signal back through a bridge-rectified supply line as a modulated current. One of those things that are obvious when someone else does it...
A bit off topic, but did you see Design Note 230? It shows a neat trick on how to make a differential amplifier with high common mode range without sacrificing gain. Here's the description:
-------------------------------------------------------------------- "Measuring small voltages on top of large voltages can be quite difficult. Often, the standard difference amplifier topology is implemented with very high value input resistors and low value divide and feedback resistors, as shown in Figure 2. However, this results in significant differential mode attenuation."
"The circuit in Figure 3 uses an LT1884 to achieve high common mode input range and rejection without sacrificing differential gain." --------------------------------------------------------------------
Here's the url for DN230.PDF. You may have to rename while saving:
Here's a shorter version in case the above doesn't work in your browser:
That's what I was hoping for too :-) but I think I may have the answer now (see below).
I'm using a Marconi 2382, which is up to the job, and, yes I did the
I'm now pretty sure the close-in phase noise is due to my loop filter circuit.
This article is very good
It derives that equation for nV/sqrt(Hz) --> dBc/Hz
With a VCO tuning sensitivity of 2.58 MHz / volt, it only requires a few nV/sqrt(Hz) to put -75dBc/Hz (my current figure) on the carrier.
Between the op-amp and the VCO, I have an RC pole comprising 1k resistor and
100n capacitor. The thermal noise of this resistor alone accounts for -82dBc/Hz ! I'm going to swap them for 100 ohm and 1uF. I'm also going to try an AD797 op-amp which has much lower noise and higher PSRR than the NE5534 I'm using at the moment. My power supply decoupling isn't that great on the op-amp at the moment either. Also, I didn't mention in my earlier posts, but close-in phase noise was even worse until I replaced an OP42FZ with the NE5534 and put a 100uF decoupling cap on the + input.
I'm not 100% sure about this, but a possible explanation for the plateau is that:
op-amp input noise voltage tends to fall from DC up to (typ) 1KHz (above that it levels off)
My loop's dynamics apply a 40dB/decade rising response to noise injected at the loop filter output **
The nV/sqrt(Hz) --> dBc/Hz formua has fos on the bottom, so it applies a falling response The sum total of these three is a flat(ish) close-in noise level.
** Put a summer at the loop filter output. The output of the summer is the tuning voltage vt. Inject noise thetaN into the summer. Do a Bode plot of vt/thetaN and it's a high-pass, rising at 40dB per decade, and then 0dB above the loop natural frequency.
Correction: below the loop BW the output phase noise *should* be determined by the reference - unless some idiot has put a really noisy loop filter in there (see my other post).
Unfortunately, Mini-Circuits only specify it at 1, 10 and 100 KHz.
They quote -86dBc/Hz at 1 KHz.
I disagree with you here: Firstly, 200 Hz is well inside loop BW and therefore under the control of the loop. Secondly, the usual cause of the plateau is not that loop gain and VCO phase noise balance one another. It is - as you said earlier - that phase noise inside loop BW *should* be that of the reference multiplied; and reference phase noise is flat except at very small offsets.
Originally, the PLL was much noisier. I got 10dB improvement by altering the VCO buffer/limiter, and 10dB cleaning up the loop filter; however, there was no further improvement with the 100 ohm resistor, and only a dB or 2 for the AD797.
Annoyingly, the 797 doesn't like acquiring lock, but I managed to persuade it for the purpose of the test! I see it has a differential input resistance of only 7.5k, which may be upsetting my loop filter. That's for later...
Next, following suggestions made in another thread, I'm going to replace my rather dubious VCO buffer / limiter with a couple of HCU04 gates. If I can just get it down another 10dB, I'll be satisfied.
I'm not too surprised. Again, there is no magic place where your VCO's noise contribution stops and the opamp's begins. Control-wise, it looks like one big varactor-tuned tank circuit driven by a phase detector. Sure, there are one or more additional poles, but I don't see a reason why their exact position in the circuit should make any difference, as long as the loop isn't way underdamped. (Meaning, as long as it actually has the gain needed to establish dominance over the spectral content within the loop bandwidth as defined by the lowest-frequency pole).
Well, that, or the XOR type phase detector. If you switch to a true PFD, your acquisition problems may go away.
An ideal opamp for PLL work would have no input bias current and no noise. It wouldn't load the phase detector (or its charge pump) at all. (It would also, as an app note I saw the other day suggests, cost $0.00 in quantities of 10 and up. :)
I know you got some good advice from Win Hill and some other folks on that, and I'm far from qualified to debate it with them, but I really am not a fan of (mis)using HC TTL gates as buffers. You want a buffer, use a buffer chip or a diff amp. The microwave guys in the Amateur community have been having all sorts of fits with a popular reference- lock board lately because a 'clever' TTL buffer application proved dependent on chips from one particular manufacturer. That's not the first time I've heard of circuits coming to grief that way.
When I need to drive a TTL counter or something, I usually just use a grounded-emitter bipolar with 10K resistors on either side of the base and a 680-ohm collector load resistor to +5. The analog signal comes in through a 0.1 uF capacitor to the base. A 10-20 MHz input signal is fine down to -10 dBm or so with an ordinary 2N2222, and you get a signal at the collector that can drive TTL directly.
It would probably earn a place on one of Win's famous "BAD!" circuit pages for one reason or another, but, hey, it survived at least one design review at Tektronix... and it's not going to break when someone decides to make their 2N2222s a little bit differently.
Ah! Thanks. Theoretically, the open loop gain passes through 0dB around 175 Hz and is still under 6dB at 100 Hz. So there isn't much loop gain to correct the noise around the offsets I'm concerned about.
Actually, it's an AD9901-style PFD which only reduces to XOR-mode when the frequencies are close.
Next time, I'll probably buy a 5V VCO or roll my own.
Did they use HCU i.e. un-buffered gates?
I'm pleased with my new buffer/limiter. It's a lot simpler than what I had before, takes up less space, and the waveforms look great. It hasn't made a dent on the phase noise - yet; however, whilst tinkering, I noticed the tuning voltage slews much slower than I would expect given the (theoretical) loop bandwdith. I changed a 22k resistor between the PFD output and the op-amp summing node to 4k7, the slew rate increased, and the phase noise dropped to -80dBc/Hz. Result! I need more loop gain.
Embarassingly, I actually have two 22k resistors (split 44k with small cap) between the PFD output and the op-amp summing node to reduce loop gain. The reason for this was to keep loop bandwidth down to prevent reference spurs, and I used them to control the 0dB cross-over point.
The thermal noise of 44k is 27nV/sqrt(Hz). With only 6dB loop gain at
100Hz, that's not helping. Added to the op-amps input noise, and a bit from the 1k resistor on the output, it starts to look like I can account for the noise levels I'm seeing.
I really want to get rid of those noisy 22k resistors and I have an idea, which I'll try tonight, that might do it. Failing that, another option might be to increase the loop bandwdith: trading close-in phase noise for reference supression. At the moment, theoretically, the comparison frequency is down -146dB between the PFD output and the VCO. I probably don't need that much suppresion!
Neat! Sounds like the loop was still getting quieter at the 200 Hz offset where you measured it. The smaller resistances and quieter opamp should still pay off at wider offsets, so they're more than worthwhile.
I've re-designed the loop filter for wider bandwidth, using small resistors, and the close-in phase noise is now down to -86dBc/Hz rising to a peak of -82dBc/Hz at a 500Hz offset. This agrees with a SCILAB design prediction of a 4dB peaking in closed-loop response. Now that I actually have some loop gain at 50 Hz to reject line frequency, I no longer have to operate the PLL in a screened box to see this performance! I'm thrilled. Thanks for triggering the eureka moment earlier. The problem was simply a lack of loop gain. I can't believe I was so dumb not to realise it.
I couldn't tell if the second design is also meant for use up to 150 MHz with the BFT92 diff pair.
I didn't have much luck with my diff pair, using surplus BF679S devices (ft ~ 1 GHz) of dubious origin. Coincidentally, I've got an unopened pack of BFT93 here (ordered at the same time as the AD797) which I might try.