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AN535 Datasheet(PDF) 6 Page - Motorola, Inc |
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AN535 Datasheet(HTML) 6 Page - Motorola, Inc |
6 / 12 page AN535 6 MOTOROLA SEMICONDUCTOR APPLICATION INFORMATION Figure 7. Phase-Locked Loop Circuit Parameters fi Phase Detector Kp Programmable Counter Kn Filter Kf VCM Ko fo ( 42 ) N min + fo min fi + fo min fstep + 2MHz 100KHz + 20 ( 43 ) N max + fo max fstep + 3MHz 100KHz + 30 ( 44 ) Kn + 1 20 to 1 30 A type 2 system is required to produce a phase coherent output relative to the input (See Table 1). The root locus contour is shown in Figure 5 and the system step response is illustrated by Figure 6. The operating range of the MC4024/4324 VCM must cover 2MHz to 3MHz. Selecting the VCM control capacitor according to the rules contained on the data sheet yields C = 100pF. The desired operating range is then centered within the total range of the device. The input voltage versus output frequency is shown in Figure 8. Figure 8. MC4324 Input Voltage versus Output Frequency (100pF Feedback Capacitor) 5.5 6.0 fout, OUTPUT FREQUENCY (MHz) 5.0 4.0 3.0 2.0 1.0 0 5.0 4.0 3.0 2.0 1.0 0 VCC = 5.0 Vdc +125°C -55°C +25°C -55°C +25°C +125°C The transfer function of the VCM is given by: ( 45 ) Ko + Kv s Where Kv is the sensitivity in radians per second per volt. From the curve in Figure 8, Kv is found by taking the reciprocal of the slope. Kv + 4MHz * 1.5MHz 5V * 3.6V 2 p rad s V Kv = 11.2 x 106 rad/s/V ( 46 ) Thus Ko + 11.2 x106 s rad s V ( 47 ) The s in the denominator converts the frequency characteristics of the VCM to phase, i.e., phase is the integral of frequency. The gain constant for the MC4044/4344 phase detector is found by5 Kp + DFHigh * UFLow 2(2 p) + 2.3V * 0.9V 4 p + 0.111V rad ( 48 ) Since a type 2 system is required (phase coherent output) the loop transfer function must take the form of Equation 19. The parameters thus far determined include Kp, Ko, Kn leaving only Kf as the variable for design. Writing the loop transfer function and relating it to Equation 19 G(s)H(s) + Kp Kv Kn Kf s + K(s ) a) s2 ( 49 ) Thus, Kf must take the form Kf + s ) a s ( 50 ) in order to provide all of the necessary poles and zeroes for the required G(s) H(s). The circuit shown in Figure 9 yields the desired results. Figure 9. Active Filter Design R1 R2 C A Freescale Semiconductor, Inc. For More Information On This Product, Go to: www.freescale.com |
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