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ML12179 Scheda tecnica(PDF) 7 Page - LANSDALE Semiconductor Inc. |
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ML12179 Scheda tecnica(HTML) 7 Page - LANSDALE Semiconductor Inc. |
7 / 11 page www.lansdale.com Page 7 of 11 Issue A LANSDALE Semiconductor, Inc. ML12179 Legacy Applications Information Appendix: Derivation of Loop Filter Transfer Function The purpose of the loop filter is to convert the current from the phase detector to a tuning voltage for the VCO. The total transfer function is derived in two steps. Step 1 is to find the voltage gen- erated by the impedance of the loop filter. Step 2 is to find the transfer function from the input of the loop filter to its output. The “voltage” times the “transfer function” is the overall transfer function of the loop filter. To use these equations in determining the overall transfer function of a PLL multiply the filter's imped- ance by the gain constant of the phase detector then multiply that by the filter's transfer function (which is unity in the 2nd and 3rd order cases below). Figure 10. Transfer Function for the Crystal Noise in the Frequency Plane Figure 11. Transfer Function for the VCO Noise in the Frequency Plane T(j ω= • )N 1+ j 2 ζ o ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω 1 ( (( ( ( ( ( ( ( ( ( ( +– + +– K3K4 4 o4 B 2 o2 j2 ζ () o (AK4 K5) 3 o3 T(j ω= ) K3K4 4 o4 B – 2 o2 j –+ (AK4 K5) 3 o3 1+ – – K3K4 4 o4 B 2 o2 j ++ 2 ζ o (AK4 K5) 3 o3 Figure 12. Overall Transfer Function of the PLL For the 2nd Order PLL: Vp Co Ro Vt ZLF(s) RoCos1 Cos TLF(s) Vt(s) Vp(s) 1, == = = + Vp(s) Kp(s)ZLF(s) For the 3rd Order PLL: Vp Co Ro Vt ZLF(s) RoCos1 + CoRoCas2 (Co Ca)s ++ TLF(s) Vt(s) Vp(s) 1, = = = = Vp(s) Kp(s)ZLF(s) Ca For the 4th Order PLL: Vp Co Ro Vt ZLF(s) = (RoCos1) ++ (RxCxs1) CoRoCaRxCxs3 [ ++ + + + + + (Co Ca)RxCx CoRo(Cx Ca) ] s2 (Co Ca Cx)s TLF(s) = = Vt(s) Vp(s) 1 (RxCxs1) + ,Vp(s) = Kp(s)ZLF(s) Ca Rx Cx |
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