文档介绍：PRINCIPLES OF PHASE LOCKED LOOPS
(PLL)
(TUTORIAL)
VĚNCESLAV F. KROUPA
INSTITUTE OF RADIO INGINEERING
AND ELECTRONICS
ACADEMY OF SCIENCES OF THE
CZECH REPUBLIC
Introduction
In recent years, munications in high Megahertz and low Gigahertz
frequency ranges are booming. Behind this achievements was the technological
progress in integrated circuitry on one hand and application of frequency
synthesis on the other hand.
I. Principles
The task of the phase locked loops is to maintain coherence between input
(reference) signal frequency, fi, and the respective output frequency, fo, via
parison. The theory is explained in many textbooks [., 1, 2] and
practically in all books on frequency synthesis. [3 through 10]. Here, we shall
repeat, in short, all major features with some new achievements.
A/ Basic equations
Each PLL loop works as a feedback system shown in Fig. 1.
Fig. 1 Basic work of PLL
1
To get more insight into the PLL properties, we shall simplify,
without any loss of generality, the block diagram to that shown in Fig. 2.
and introduce the Laplace transfer functions of the individual building
circuits - suitable for investigation of small signal properties.
Fig. 2 Simplified block diagram of the PLL with individual transfer
functions
Investigation of the above figure reveals that the input phase Π(t) is
Πi
compared with the output phase o(t) in phase detector (ring modulator,
sampling circuit, etc.).
(1)
_
the proportionality factor, Kd [volt/2 ], is called the "phase detector
gain."
2
Next, vd(t) passes the loop filter, F(s)
(2)
where hf(t) is the time response of the loop filter. After applying v2(t) on
the frequency control element of the voltage controlled oscillator (VCO) we
get the output phase
(3)
_
the proportionality factor, Ko [2 Hz/volt], is the oscillator gain.
Since, in most cases, Kd and Ko are voltage dependent the general
mathematical model of a PLL is a