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SP8854 Datasheet(PDF) 11 Page - Mitel Networks Corporation |
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SP8854 Datasheet(HTML) 11 Page - Mitel Networks Corporation |
11 / 13 page 11 SP8854E Fig. 8 Third order loop filter circuit diagram Loop Filter Design Generally, the third order filter configuration shown in Fig. 8 gives better results than the more commonly used second order because the reference sidebands are reduced. Three equations are required to determine values for the three constants, where The equations are: t 1 = C1R1 t 2 = R2 (C11C2) t 3 = C2R2 …(2) …(3) …(1) t 2 = 1 vn2t3 2 2 tan F0 1 t 3 = vn t 1 = KfK0 vn2N 11 vn 2 t 2 2 11 vn 2 t 3 2 1 2 1 cos F0 where Kf is the phase detector gain factor in mA/radian K0 is the VCO gain factor in radians/seconds/V N is the division ratio from VCO to reference frequency vn is the natural loop frequency F0 is the phase margin, normally set to 45° Since the phase detector used is linear over a range of 2 p radians, the phase detector gain is given by: These values can now be substituted in equation (1) to obtain a value for C1 and in equations (2) and (3) to determine values for C2 and R2. Example Calculate values for a loop with the following parameters: Frequency to be synthesised 1000MHz Reference frequency 10MHz Division ratio 1000MHz/100MHz = 100 K0 VCO gain factor 2p310MHz/V F0 phase margin 45 ° Phase comparator current 6·3mA The phase detector gain factor Kf = 6·3/2p = 1mA/radian mA/radian Phase comparator current setting 2 p Kf = From equation (3): 2 tan 45 °1 t 3 = 100kHz32p 1 cos 45 ° ∴t 3 = 659310 2 9 = 628319 0·4142 t 2 = (100kHz32p)23659310 2 9 1 ∴t 2 = 3·844310 2 6 Using these values in equation (1): t 1 = 1003(100kHz32p)2 1310 2 332p310MHz/V 3 [A] 11 vn 2 t 2 2 11 vn 2 t 3 2 where A = = 1 2 11(100kHz32p)23(3·844310 2 6)2 11(100kHz32p)23(659310 2 9)2 t 1 = ∴t 1 = 3·84310 2 9 From equation (2): = 1·59310 2 932·415 39·48310 2 12 62832 6·833 1·1714 1 2 Substituting for C2: 3·844310 2 6265931029 t 2 = R2 C11 t 3 R2 = 0·0153310 2 6 ∴R 2 = 829·4Ω = 659310 2 9 829·4 t 3 = C2R2 = t 3 R2 ∴C 2 = 0·794nF Now, t 1 = C1 ∴ C 1 = 3·84nF t 2 = R2 (C11C2) t 2 = C2R2 t 22t3 C1 or, R2= − + C1 R2 C2 FROM CHARGE PUMP TO VCO FROM CHARGE PUMP REFERENCE |
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