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pll-for-high-frequency-receivers-and-transmitters-2.pdf
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本文侧重于详细考察与PLL相关的两个关 键技术规格:相位噪声和参考杂散。导致相位噪声和参考杂 散的原因是什么,如何将其影响降至最低?讨论将涉及测量 技术以及这些误差对系统性能的影响。我们还将考虑输出漏 电流,举例说明其在开环调制方案中的重要意义。
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Analog Dialogue 33-5 (© 1999 Analog Devices) 1
Phase-Locked Loops
for High-Frequency
Receivers and
Transmitters–Part 2
by Mike Curtin and Paul O’Brien
The first part of this series of articles introduced the basic concepts
of phase-locked loops (PLLs). The PLL architecture and principle
of operation was described and accompanied by an example of
where a PLL might be used in a communication system.
In this second part, we will focus on a detailed examination of two
critical specifications associated with PLLs: phase noise and reference
spurs. What causes them and how can they be minimized? The
discussion will include measurement techniques and the effect of
these errors on system performance. We will also consider output
leakage current, with an example showing its significance in open-
loop modulation schemes.
Noise in Oscillator Systems
In any oscillator design, frequency stability is of critical importance.
We are interested in both long-term and short-term stability. Long-
term frequency stability is concerned with how the output signal
varies over a long period of time (hours, days or months). It is
usually specified as the ratio, ∆f/f for a given period of time,
expressed as a percentage or in dB.
Short-term stability, on the other hand, is concerned with variations
that occur over a period of seconds or less. These variations can be
random or periodic. A spectrum analyzer can be used to examine
the short-term stability of a signal. Figure 1 shows a typical
spectrum, with random and discrete frequency components
causing a broad skirt and spurious peaks.
Frequency
Amplitude
Random Noise Fluctuation
Discrete Spurious Signal
f
0
Figure 1. Short-term stability in oscillators.
The discrete spurious components could be caused by known clock
frequencies in the signal source, power line interference, and mixer
products. The broadening caused by random noise fluctuation is
due to phase noise. It can be the result of thermal noise, shot noise
and/or flicker noise in active and passive devices.
Phase Noise in Voltage-Controlled Oscillators
Before we look at phase noise in a PLL system, it is worth
considering the phase noise in a voltage-controlled oscillator (VCO).
An ideal VCO would have no phase noise. Its output as seen on a
spectrum analyzer would be a single spectral line. In practice, of
course, this is not the case. There will be jitter on the output, and
a spectrum analyzer would show phase noise. To help understand
phase noise, consider a phasor representation, such as that shown
in Figure 2.
ω
o
ω
m
∆θ
rms
V
N
rms
V
SPK
Figure 2. Phasor representation of phase noise.
A signal of angular velocity ω
O
and peak amplitude V
SPK
is shown.
Superimposed on this is an error signal of angular velocity ω
m
.
∆θrms represents the rms value of the phase fluctuations and is
expressed in rms degrees.
In many radio systems, an overall integrated phase error
specification must be met. This overall phase error is made up of
the PLL phase error, the modulator phase error and the phase
error due to base band components. In GSM, for example, the
total allowed is 5 degrees rms.
Leeson’s Equation
Leeson (see Reference 6) developed an equation to describe the
different noise components in a VCO.
L
FkT
AQ
f
f
PM
L
O
m
≈
10
1
8
2
2
log
(1)
where:
L
PM
is single-sideband phase noise density (dBc/Hz)
F is the device noise factor at operating power level A (linear)
k is Boltzmann’s constant, 1.38 × 10
–23
J/K
T is temperature (K)
A is oscillator output power (W)
Q
L
is loaded Q (dimensionless)
f
O
is the oscillator carrier frequency
f
m
is the frequency offset from the carrier
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