74HCT9046A Datasheet, PDF (34/43 Pages) NXP Semiconductors – PLL with bandgap controlled VCO

NXP Semiconductors
74HCT9046A
PLL with band gap controlled VCO
74HCT9046A_6
Product data sheet
K _p = ₄-----_×⁵-----_π-- = 0.4 V ⁄ r
Using PC2 with the passive filter as shown in Figure 34 results in a high gain loop with the
same performance as a loop with an active filter. Hence loop filter equations as for a high
gain loop should be used. The current source output of PC2 can be simulated then with a
fictive filter resistance:
R3‘ = -^R---₁^b---₇ⁱ--^a--^s
The transfer functions of the filter is given by:
K _f = ¹-----⁺_s---_τ--^s-₂--^τ--²-
Where:
τ₁ = R3‘ × C2
τ₂ = R4 × C2
The characteristic equation is: 1 + K _p × K _f × K_o × K_n
This results in:
1
+
K
p


1_-----+_s---τ--s_-1--τ_{--2-}
K_-----v
s
K
n
=
0
or:
s² + sK _pK _vK _n^ττ---²¹- + K _pK _vK _n ⁄ τ₁ = 0
This can be written as:
s² + 2ξω_ns + (ω_n)² = 0
with the natural frequency ω_n defined as:
ω_n = ^K-----^p----^×-----^K-_τ--₁--^v---^×-----^K----ⁿ-
and the damping value given as: ζ = 0.5 × τ₂ × ω_n
In Figure 35 the output frequency response to a step of input frequency is shown.
The overshoot and settling time percentages are now used to determine ω_n.
From Figure 35 it can be seen that the damping ratio ζ = 0.707 will produce an overshoot
of less than 20 % and settle to within 5 % at ω_nt = 5. The required settling time is 1 ms.
This results in:
Rev. 06 — 15 September 2009
© NXP B.V. 2009. All rights reserved.
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