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MC13175D Datasheet(PDF) 8 Page - Motorola, Inc |
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MC13175D Datasheet(HTML) 8 Page - Motorola, Inc |
8 / 17 page MC13175 MC13176 8 MOTOROLA RF/IF DEVICE DATA Figure 11. Block Diagram of MC1317XD PLL fo = nfi N = 8 : MC13175 N = 32 : MC13176 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: Loop Filtering The fundamental loop characteristics, such as capture range, loop bandwidth, lock–up time and transient response are controlled externally by loop filtering. The natural frequency ( ωn) and damping factor (∂) are important in the transient response to a step input of phase or frequency. For a given ∂ and lock time, ωn can be determined from the plot shown in Figure 12. 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 For ∂ = 0.707 and lock time = 1.0 ms; then ωn = 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/s2). 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 ∂. The equations t1 = R1C and t2 = R2C are related in the loop filter transfer functions F(s) = 1 + t2s/1 + (t1 + t2)s. Figure 13. Lag–Lead Low Pass Filter VO C R2 R1 Vin 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 damping factor, ∂ = (ωn/2) (t2 + 1/Kv) Rewriting the above equations and solving for the MC13176 with ∂ = 0.707 and ωn = 5.0 k rad/sec: Kv = KpKoKn = (30) (0.91 106) (1/32) = 0.853 106 t1 + t2 = Kv/ωn2 = 0.853 106/(25 106) = 34.1 ms t2 = 2∂/ωn = (2) (0.707)/(5 103) = 0.283 ms t1 = (Kv/ωn2) – t2= (34.1 – 0.283) = 33.8 ms |
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