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MC13176D Scheda tecnica(PDF) 7 Page - LANSDALE Semiconductor Inc. |
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MC13176D Scheda tecnica(HTML) 7 Page - LANSDALE Semiconductor Inc. |
7 / 16 page Figure 11. Block Diagram of ML1317x PLL fo = nfi N = 8 : ML13175 N = 32 : ML13176 Kn = 1/N Divider θo(s) Pins 13,14 Ko = 0.91Mrad/sec/µA Amplifier and Current Controlled Oscillator Pin 6 Low Pass Filter Kf θn(s) = θo(s)/N Pin 7 θe(s) Kp = 30 µA/rad Phase Detector fn = fo/N Pins 9,8 fi = f ref θi(s) Kp Kf Kn Ko Ko = Phase detector gain constant in = µA/rad; Kp = 30 µA/rad = Filter transfer function = 1/N; N = 8 for the MC13175 and = 1/N; N = 32 for the MC13176 = CCO gain constant in rad/sec/ µA = 9.1 x 105 rad/sec/ µA Where: LANSDALE Semiconductor, Inc. ML13175/ML13176 LOOP FILTERING The fundamental loop characteristics, such as capture range, loop bandwidth, lock–up time and transient response are con- trolled externally by loop filtering. The natural frequency ( ωn) and damping factor (L ) are important in the transient response to a step input of phase or frequency. For a givenL and lock time wn can be determined from the plot shown in Figure 12. For L = 0.707 and lock time = 1.0 ms; then ω = 5.0/t = 5.0 krad/sec. The loop filter may take the form of a simple low pass filter or a lag–lead filter which creates an additional pole at origin in the loop transfer function. This additional pole along with that of the CCO provides two pure integrators (1/s 2 ). In the lag–lead low pass network shown in Figure 13, the values of the low pass filtering parameters R1, R2 and C determine the loop constants ωn and L. The equations t1=R1 C and t2=R2C are related in the loop filter transfer functions F(s) = 1 + t2s/1 + (t1 +t2)s. The closed loop transfer function takes the form of a 2nd order low pass filter given by, H(s )= KvF(s)/s + KvF(s) From control theory, if the loop filter characteristic has F(0) = 1, the DC gain of the closed loop, Kv is defined as, Kv = KpKoKn and the transfer function has a natural frequency, ωn = Kv/t1 + t2)1/2 and a dampning factor, L = ( ωn/2) (t2 + 1Kv) Rewriting the above equations and solving for the ML13176 with L = 0.707 and ωn = 5.0 k rad/sec. Kv = KpKoKn = (30) (0.91 X 10 6)(1/32) = 0.853 X 106 t1 + t2 = Kv/ωn2 = 0.853 X 10 6/(25 X 106) = 34.1 ms t2 = 2L /ωn = (2)(0.707)/(5 X 10 3) = 0.283 ms t1 = (Kv/ωn2) –t2=(34.1–0.283) = 33.8 ms Legacy Applications Information Figure 12. Type 2 Second Order Response 0 ωnt 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10 11 12 13 0.8 1.9 0.4 0.6 0.7 0.2 0.3 0.5 1.5 2.0 ζ = 0.1 1.0 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Figure 13. Lag–Lead Low Pass Filter VO C R2 R1 Vin www.lansdale.com Page 7 of 16 Issue c |
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