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SP8858IGHCAR Datasheet(PDF) 11 Page - Mitel Networks Corporation |
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SP8858IGHCAR Datasheet(HTML) 11 Page - Mitel Networks Corporation |
11 / 17 page 11 SP8858 The selection of C1 and R1 is often approached by using the standard representation for the second order characteristic equation: s212 zvn1vn2 and selecting the natural-loop frequency and the damping factor z to give the desired response. The time constants are calculated using: 2 zvn = t1K/C1 and vn2 = K/C1 so that C1 = K/ vn2 and R1 = 2zvn/K Alternatively, the loop filter and formula shown in Fig. 10b can be used to introduce a pole in F(s) at 21/ t2 which will provide additional roll-off in the closed loop transfer characteristic in order to attenuate the reference sidebands. The closed loop transfer function becomes: higher order loops to use CAD tools to assess stability. Popular analysis tools taken from control theory, such as root locus and Bode diagrams, are useful to aid the design of the closed loop PLL system. AN194 describes these tools in more detail and introduces a loop filter design methodolgy aimed at optimising the phase noise performance. Loop filter design example Use the demonstration board to generate a 1GHz signal with a resolution of 500kHz (N = 5000) and reference oscillator frequency of 40MHz. Set natural loop frequency, vn, to 2 p3104 rad/s and damping factor to 0·7. The MQE001-1016 VCO gain, KVCO, is nominally 25MHz/V. Set the phase detector output current to 2mA so that KPD = 2310 2 3/2p A/rad. Using the above formula, calculate the loop filter R and Cs. K = 2 p32531063231023/2p35000 = 10 C1 = 10/(2 p3104)32 ≈ 2·531029 R1 = 230·732p3104/10 ≈ 8796 C2 = C1/10 ≈ 0·2531029 Realise the loop filter with C1 = 2·2nF, C2 = 220pF and R1 = 8·2k Ω. The single sideband phase noise specturm for this example is shown in Fig. 11. − + C1 R1 C2 Ii(s) Vo (s) Vo (s) / Ii(s) = [s(t11t2)11]/sC1(st211) where t1 = C1R1 and t2 = C2R1 − + C1 R1 Ii(s) Vo (s) Vo (s) / Ii(s) = [s(t111]/sC1 where t1 = C1R1 Fig. 10a Fig. 10b Fig. 10 Loop filters 0 2 10 2 20 2 30 2 40 2 50 2 60 2 70 2 80 2 90 2 100 2 110 2 120 2 130 2 140 2 150 2 160 2 170 10Hz 100Hz 1kHz 10kHz 100kHz FREQUENCY Fig. 11 Care must be taken when choosing C2 to ensure that the additional pole does not unduly affect the stability margins of the loop. In practice, a simple and useful rule of thumb is to set the desired second order response as above and then set C2 to be 1/10 of C1. It is advisable when designing third order or [s( t11t2)11]KVCOKPD [C1 t2s31C1s21K(t11t2)s1K] fo(s) fi(s) = |
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