74HC7046A Datasheet, PDF (36/38 Pages) NXP Semiconductors – Phase-locked-loop with lock detector

Philips Semiconductors
Phase-locked-loop with lock detector
Product specification
74HC/HCT7046A
PLL design example
The frequency synthesizer, used in the design example
shown in Fig.34, has the following parameters:
Output frequency: 2 MHz to 3 MHz
frequency steps : 100 kHz
settling time : 1 ms
overshoot
: < 20%
The open-loop gain is H (s) x G (s) = K_p × K_f × K_o × K_n.
Where:
K_p = phase comparator gain
K_f = low-pass filter transfer gain
K_o = K_v/s VCO gain
K_n = 1/n divider ratio
The programmable counter ratio K_n can be found as
follows:
N_min. = _f--fs--^o-_t--^ue--^tp- = _{1---2-0---0-M-----kH---H--z--z-} = 20
N_max. = _f--fs--^o-_t--^ue--^tp- = _{1---3-0---0-M-----kH---H--z--z-} = 30
The VCO is set by the values of R1, R2 and C1,
R2 = 10 kΩ (adjustable). The values can be determined
using the information in the section “DESIGN
CONSIDERATIONS”.
With f_o = 2.5 MHz and f_L = 500 kHz this gives the following
values (V_CC = 5.0 V):
R1 = 10 kΩ
R2 = 10 kΩ
C1 = 500 pF
The VCO gain is:
K_V = _{0----.--9----2–}----f--^L₍--V--^×---_C--2-_C----^×-_–---^π--0---.--9---₎-- = = ^{1-----3-M---.-2-H----z--} × 2π ≈ 2 × 10⁶ r/s/v
The gain of the phase comparator is:
K_p = _4-V----×-^C---^C-_π-- = 0.4 V/r.
The characteristics equation is:
1 + H (s) × G (s) = 0.
This results in:
s² + ^1-----+-----K-----^p--₍--^×τ---₁-K---₊--^v---_τ×---₂--K-₎---ⁿ----^×-----^τ---²- s + -K----^p-₍--_τ-^×--₁---K-₊---^v--_τ--^×-₂---₎^K-----n = 0.
The natural frequency ω_n is defined as follows:
ω_n = -K----^p-₍--_τ-^×--₁---K˙-₊---^v--_τ--^×-₂---₎^K-----n.
and the damping value ζ is defined as follows:
ζ = _2----1ω-----_n- × -1----⁺-----K----^p-----^×τ---₁-K---₊--^v---_τ×---₂--K----ⁿ----^×-----^τ---²- .
The overshoot and settling time percentages are now used
to determine ω_n. From Fig.35 it can be seen that the
damping ratio ζ = 0.8 will produce an overshoot of less
than 20% and settle to within 5% at ω_nt = 4.5. The required
settling time is 1 ms. This results in:
ω_n = ^5-t- = _{0----.--05---0---1--} = 5 × 10³ r/s.
Rewriting the equation for natural frequency results in:
(τ₁ + τ₂) = ^K-----p----^×--_ω---K-_n---^v--₂--^×----K-----ⁿ .
The maximum overshoot occurs at N_max.:
(τ₁ + τ₂) = -0--5-.--40----0^×---0--2-₂----^××-----13---0-0---⁶- = 0.0011 s.
When C2 = 470 nF, then
R4 = --⁽--^τ---¹----⁺-----^τ-K--²--_p-⁾---_×-^×----K-2---_v--^×--_×---^ω--K--ⁿ--_n--^×-----^ζ----^–-----1- = 790 Ω.
R3 is calculated using the damping ratio equation:
R3 = _C--^τ---¹_2-- – R4 = 2 kΩ.
The transfer gain of the filter is given by:
K_f = -1----₊-----1-₍---_τ-⁺--₁---^τ-₊-²---s-_τ---₂--₎----s-
Where:
τ₁ = R3C2 and τ₂ = R4C2.
December 1990
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