PLL Charge pump phasefrequency detector CPPFD has a maximum

PLL

Charge pump phase-frequency detector (CPPFD) has a maximum output current of I_cp = 5mu A for 2pi radians of phase difference. For the voltage controlled oscillator (VCO) in the system, the V-f measurements in the table were obtained. Since the VCO voltage-to-frequency characteristic is nonlinear, the VCO tuning gain Kvco changes as a function of VCO control voltage Vctl- Estimate (accuracy plusminus 10%) the minimum and maximum values of K_o over the voltage tuning range. You are asked to analyze the loop dynamics for loop bandwidth//; and stability. remember that to ensure adequate phase margin for loop stability, the magnitude plot of the loop gain (loop transmission) |T(f)| must meet two requirements: At the unity loop gain frequency fu, the magnitude plot of the loop transmission |T(f)| must cross OdB at a slope of~ -20dB/decade, and any pole or zero in the loop transmission T(f) must be at least a factor of 10X away from the loop bandwidth frequency. With an input frequency of 20MHz (at which Kvco = 4 MHz/V) and R_z, C_1, and C_2 values as shown, determine the unity loop gain frequency fu and phase margin

Solution

a) for a given voltage tuning range K_vc0(min)   = 24.4/4.5=5.42MHz/V

K_vc0(max)=8.4/0.5=16.8MHz/V