Say I am trying to demodulate a message up to 25kHz in frequency, with a peak frequency deviation of 75kHz and a carrier of 1MHz, implying a 200kHz bandwidth using carsons rule.
Would I design the transfer function of the loop (Output/Input) so that there is a 20dB/decade slope up to 25kHz* where I would want it to level off? Should this "level" point be unity gain?
While trying to develop the loop transfer function, I find it possible to end the 20dB/decade slope at 25kHz* and level out, but I find that it is impossible to design it so that the level out point is unity gain as well. In fact, I can never get unity gain anywhere near 25kHz*.
edit: This seems to be because I do not understand how to measure the Kvco constant. Is this constant controllable, or a natural element of the VCO? In derivations I find, it is treated as a separate entity than Av (the VCO carrier amplitude) and appears as a result of linearizing the PLL in most derivations.
If I can't control the value of this constant then it seems that I will never be able to achieve unity gain at the desired frequency as the rest of the constants (Ac,Av,Au,Kd) influence both the numerator and denominator of the transfer function, thus changing the frequency at which level gain occurs but not the magnitude of the gain itself.
edit2: Is the Kvco constant the frequency deviation in Hz/V? If this is the case, does it need to match the frequency deviation of the incoming FM modulated signal? I believe it would, in which case it becomes a fixed value. If it is a fixed value, does this not limit the design of the PLL? For example, in order to achieve unity gain at high frequencies, the numerator of the transfer function below seems to need to be 0.5 so that at very large values of s, the function essentially becomes 1. If this is the case, I can no longer change the bandwidth of the 20dB/decade region as it has become fixed if I want unity gain.
Here is my short Matlab simulation code for trying to design this transfer function:
%LOOP TF GAIN CALCULATION TESTING %================================= %PLL DESIGN INFORMATION: %75kHz Peak Frequency Deviation %1MHz carrier %Baseband message bandwidth ~= 25kHz %Phase Detector LPF cutoff: 500kHz, 4th order butterworth %=========================================================== %Set Constants for loop calculation: kvco = 1; %VCO constant Au = 150000; %Amplifier Gain kd = 1; %Phase detector LPF filter gain up to cutoff of ~500kHz Ac = 1; %FM Modulator Carrier Amplitude Av = 1; %VCO carrier Amplitude %================================================================= Loop_Num = [Au*kd*Ac*Av 0]; %Numerator of Transfer Function Loop_Dem = [0.5 Au*kd*Ac*Av*kvco]; %Denominator of Transfer Function Loop_Transfer = tf(Loop_Num, Loop_Dem); %Create Transfer Function figure(1) bode(Loop_Transfer) %Plot