opamp design in loop filter
How could I define an opamp bandwidth which use in loop filter of PLL. Should the opamp have high gain at PLL loop bandwidth? For example, PLL loop bandwidth is 360KHz, then opamp must have >60dB gain at 360kHz?
Thanks
wccheng
The task of the loop filter is (a) to attenuate unwanted signals and (b) to establish the desired dynamic properties of the loop.
From this, the loop filter specification is derived.
You have to select an opamp type which is able to establish the filter specification as good as necessary.
Therefore: What is your filter spec ?
dual path filter
?
A low pass filter is specified by its order resp.by its pole and zero location.
The PLL can be viewed as a simplified control loop system (Two poles and one zero) ONLY if all the other poles and zeros are much higher in frequency!
So if you have an open loop bandwidth in your PLL of 360 KHz, that is typically where you set up a zero to partially cancel the two poles in the system to give a phase margin of at least 45 degrees, and preferrably more like 60 degrees. If you are unfortunate enough to have other stray poles in the system, like say a pole in the op amp itself at around 1 MHz, then you are going to have more phase shift than desired at the 360 KHz frequency, and run the risk of having an unstable loop. You can run the numbers, but to avoid something like that happening, if my open loop bw were going to be 360 KHz, I would make sure that the unity gain in the op amp itself were at least 10 times higher, or 3.6 MHz. That way I only give up a degree or two to the parasitics.
Added after 4 minutes:
It is actually a little worse than I remember:
http://ocw.mit.edu/NR/rdonlyres/Aero.../0/ps10sol.pdf
At one thenth the pole frequency, you still get around 5 degrees of additional phase shift
Dear Sir,
Is there any special requirement for 3-dB bandwidth of opamp?
For example, 3-dB bandwidth > 360kHz ?
Thanks
Maybe you did not understand what I said. There is a field of electrical engineerig called Control Theory. This is where circuits are used, including feedback, to control something. In the PLL case, you are controlling the microwave phase of the VCO to "lock" onto a lower frequency phase of a reference. But this is really no different than controlling, say, and elevator going from one floor in a building to another. In the elevator case, you want it to smoothly start up, go to the next floor, decelerated, and not overshoot or oscillate before stopping at the next floor. Same with the PLL. You want the phase controlled, but do not want glitches, overshoots, ringing, etc if a slight phase disturbance happens. The parameters of the control circuit decide if the loop behaves well, or if it tends to have overshoot and ringing. You can choose these parameters to be well behaved by selecting resistors and capacitors in your loop filter, like any basic PLL design book will tell you how to do.
In basic control theory, you try to simplify the control circuit so that it is easy to understand, and can therefore be predicted by some simple equations. To keep the PLL as simple as possible, you want the only dominant factors to be the VCO tuning slope, and the loop filters pole and zero. Other poles and zeros can pretty much be ignored if they happen at a MUCH higher frequency.
The #1 key in any loop design is to keep it stable, and an easy snapshot (although not a complete one) is to use something called a bode plot to show the open loop gain and phase shift. It can be shown that if when the open loop gain approaches unity, that you want the phase shift to be around -120 degrees (60 degrees shy of what the circuit usually wants to do, which would be -180 degrees. If you choose your resistors and capacitors in the loop filter to do this, but you used a poor op amp with a limited bandwidth, then the op amp itself will add to the phase shift. If you cross the unity gain point and the phase shift is near -180 degrees, the control loop will be guaranteed to oscillate.
So, for your example where the open loop gain of the control loop goes to unity at 360 KHz, you would want an op amp with at least a 3 dB bandwidth of 3.6 MHz or higher.
Hi wccheng and Bif44
I think the situation (opamp bandwidth for PLL filter) is not as critical as it seems to be from the last contribution. Let me explain my sight:
1.) If the loop has locked, the output of the PLL (that means the filter input) is a more or less slowly varying voltage with a frequency equal to the difference of both frequencies (input resp. VCO). Certainly, this "beat" frequency will not approach 360 kHz.
In addition there is a frequency component nearly equal to the double of the VCO, which in any case must be suppressed as good as possible.
Thus, the parasitic opamp phase shift has to be considered for rather low frequencies only.
2.) If the loop is out of lock this opamp phase shift plays no role for the pull-in process.
3.) As a consequence, it is really NOT necessary that the "3-dB-bandwidth" of the opamp is in the MHZ range (I suppose, bif44 has ment the transit frequency !)
I think, each mid-class opamp would do the job.
Regards
LvW
Sorry, but you are completely wrong. An unstable control loop has, in effect, infinite gain at the instability frequency. Noise will build up after only a microsecond or so to the point that there is either a total unlocked oscillation, or at the best a pair of -30 dBc noise peaks in the RF spectral output.
From your comment, you might want to spend some time in the lab with a PLL, and oscilloscope, and a spectrum analyzer, and fool around with the loop filter parameters. You will learn a lot.
Hi bif44, thanks for the tip. Nevertheless, may I reply ?
(One personal/minor information for you regarding some lab experience: In the mid 70th I had the opportunity to work for some time with F.M.Gardner - and we designed PLL′s for deep space missions).
To your reply:
1.) Who spoke about an unstable loop ? For my opinion, this has nothing to do with the original question from wccheng. Do you expect instabilities or even self sustained oscillations when the parasitic opamp phase is 5 deg ?
2.) I think we all should try to answer his question and not to confuse him. In this context, I′ve found that your general remarks to the PLL tasks (in your former reply) could be very helpful for beginners.
2.) Do you really stick on your recommendation, that the 3-dB-bandwidth of the opamp should be at least 3.6 MHz ? Do you know such an amplifier ?
Hi wccheng,
perhaps the following information can be helpful for you:
There is a data sheet from NS for an operational amplifier which is designed with respect to PLL application. In this document a lot of interesting information concerning PLL application can be found - including opamp requirements.
Search under www. national.com and look for the part LM6211.
For example, this opamp is used within the LMX2430 IC from National Semiconductor.
In this application a loop filter is realized leading to a loop bandwidth of 100 kHz.