DESIGN CONSIDERATIONS
PHASE–LOCKED LOOP — LOW–PASS FILTER DESIGN
K K
VCO
φ
A)
PD
out
VCO
ω
=
=
n
NR C
R
1
1
φ
—
—
R
C
Nω
n
ζ
φ
2K K
VCO
V
φ
1
F(s) =
R sC + 1
1
PD
B)
VCO
out
K K
VCO
φ
R
ω
ζ
=
1
n
NC(R + R )
1
2
φ
—
—
R
R
2
N
φ
=
0.5
ω
R C +
2
C
V
n
K K
VCO
φ
R sC + 1
2
F(s) =
(R + R )sC + 1
1
2
R
2
K K
PD
—
C)
φ
VCO
out
ω
ζ
=
n
NCR
C
1
R
R
1
_
+
φ
R
ω
R C
n 2
A
VCO
φ
V
=
2
1
ASSUMING GAIN A IS VERY LARGE, THEN:
R sC + 1
R
2
2
C
F(s) =
R sC
1
NOTE: Sometimes R is split into two series resistors, each R ÷ 2. A capacitor C is then placed from the midpoint to ground to further
1
1
C
filter φ and φ . The value of C should be such that the corner frequency of this network does not significantly affect ω .
V
R
R
V
C
n
The φ and φ outputs swing rail–to–rail. Therefore, the user should be careful not to exceed the common mode input range of the
op amp used in the combiner/loop filter.
DEFINITIONS:
N = Total Division Ratio in feedback loop
K
φ
K
φ
(Phase Detector Gain) = V /4π for PD
DD out
(Phase Detector Gain) = V /2π for φ and φ
DD
V
R
2π∆f
∆V
VCO
VCO
K
VCO
(VCO Gain) =
2πfr
10
for a typical design w (Natural Frequency) ≈
(at phase detector input).
n
Damping Factor: ζ
1
RECOMMENDED READING:
Gardner, Floyd M., Phaselock Techniques (second edition). New York, Wiley–Interscience, 1979.
Manassewitsch, Vadim, Frequency Synthesizers: Theory and Design (second edition). New York, Wiley–Interscience, 1980.
Blanchard, Alain, Phase–Locked Loops: Application to Coherent Receiver Design. New York, Wiley–Interscience, 1976.
Egan, William F., Frequency Synthesis by Phase Lock. New York, Wiley–Interscience, 1981.
Rohde, Ulrich L., Digital PLL Frequency Synthesizers Theory and Design. Englewood Cliffs, NJ, Prentice–Hall, 1983.
Berlin, Howard M., Design of Phase–Locked Loop Circuits, with Experiments. Indianapolis, Howard W. Sams and Co., 1978.
Kinley, Harold, The PLL Synthesizer Cookbook. Blue Ridge Summit, PA, Tab Books, 1980.
AN535, Phase–Locked Loop Design Fundamentals, Motorola Semiconductor Products, Inc., 1970.
AR254, Phase–Locked Loop Design Articles, Motorola Semiconductor Products, Inc., Reprinted with permission from Electronic Design,
1987.
MC145151–2 through MC145158–2
28
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