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Keysight Technologies
Pulsed Carrier Phase Noise Measurements
Application Note
This application note discusses basic
fundamentals for making pulsed carrier phase
noise measurements. It assumes the reader is
familiar with the basic concepts of phase noise
and CW phase noise measurement techniques.
Table of Contents
3 Chapter 1
Introduction
4 Chapter 2
Fundamentals of Pulsed Carriers
Time Domain Representation
Frequency Domain Representation
10 Chapter 3
How Pulse Modulation Affects the
SSB Phase Noise of a CW Carrier
Convolution of CW Carrier Spectra and Pulsed Waveform
Spectra
Noise Aliasing With Pulse Modulation
Mathematical Equation for a Pulsed RF Carrier
Decrease in Carrier Power
Decrease in Pulsed Carrier Spectral Power
16 Chapter 4
How Pulsing the Carrier Affects the Phase Detector
Measurement Technique
System Noise Floor
Measurement Offset Range
Mixer dc Offset
Recommended Hardware Configurations
LO AM Noise Suppression
Phase Transients
Pulsed Carrier Phase Noise PRF Feedthrough
Measurements Application Minimum Duty Cycle
Summary
2
Chapter 1
Introduction This application note discusses basic fundamentals for
making pulsed carrier phase noise measurements.
Advances in RF and microwave communication technology
have extended system performance to levels previously The assumption is made that the reader is familiar with
unattainable. Design emphasis on sensitivity and selectivity the basic concepts of phase noise and CW phase noise
have resulted in dramatic improvements in those areas. measurement techniques.
However, as factors previously limiting system performance
have been overcome, new limitations arise and certain Chapter 2 reviews the fundamentals of pulsed carriers in
parameters take on increased importance. One of these the frequency and time domains. The majority of terms
parameters is the phase noise of signal sources used in used in succeeding chapters are defined throughout
pulsed RF and microwave systems. Chapter 2. Chapter 3 discusses how the single sideband
phase noise of a CW carrier is affected by the pulse
In pulsed radar systems, for example, the phase noise of modulation process. Chapter 4 discusses the effects a
the receiver local oscillator sets the minimum signal level pulsed RF carrier has on the performance of a phase
that must be returned from a target in order to be detect- detector based measurement.
able. In this case, phase noise affects the selectivity of the
radar receiver which in turn determines the effective range
of the overall system.
Since the overall dynamic range of the radar system is
influenced by the noise of the transmitted signal, it is not
only important to know the absolute noise of individual
oscillators but to know the residual or additive noise of
signal processing devices like power amplifiers and pulse
modulators. Because the final signal in most radar systems
is pulsed, making absolute phase noise measurements on
the pulsed carrier is essential to determining the overall
performance of the system.
3
Chapter 2
Fundamentals of Pulsed Carriers the amplitudes of the higher order harmonics are relatively
small, so reasonably shaped rectangular waves can be pro-
The formation of a square wave from a fundamental sine duced with a limited number of harmonics. By changing the
wave and its odd harmonics is a good way to begin a relative amplitudes and phases of the harmonics, both odd
discussion of pulsed carriers and their representation in and even, an infinite number of waveshapes can be plotted.
the time and frequency domains. To create a train of pulses (i.e., a waveform whose ampli-
tude alternates between zero and one) with a series of sine
You might recall having plotted a sine wave and its odd waves, a dc component must be added. Its value equals
harmonics on a sheet of graph paper, then adding up all the amplitude of the negative loops of the rectangular
the instantaneous values. If there were enough harmonics wave with the sign reversed.
plotted at their correct amplitudes and phases, the resultant
waveform would begin to approach a square wave. The Consider a perfect rectangular pulse train as shown in
fundamental frequency determined the square wave rate, Figure 1a, perfect in the sense that the rise time is zero
and the amplitudes of the harmonics varied inversely to and there is no overshoot or other aberrations. This pulse
their number. is shown in the time domain and if we wish to examine it
in the frequency domain it must be broken down into its
A rectangular wave is merely an extension of this principle. individual frequency components. Figure 1b superimposes
In fact, to produce a rectangular wave, the phases must the fundamental and its second harmonic plus a constant
be such that all the harmonics go through a positive or voltage to show how the pulse begins to take shape as
negative maximum at the same time as the fundamental. more harmonics are plotted.
Theoretically, to produce a perfectly rectangular wave, an
infinite number of harmonics would be required. Actually,
T
E
A
TIME
Figure 1a. Periodic rectangular pulse train
4
A spectrum analyzer would in effect "unplot" these between lines is equal to the PRF. The envelope of this plot
waveforms and present the fundamental and each harmonic follows a sinX/X function with the spectral line frequencies
in the frequency domain. a fLINE = n X 1/T, for n = 1,2,3.... Note that the nulls occur
at integer multiples of the reciprocal of the pulse width.
A frequency domain plot of this waveform would be as
shown in Figure 2. This is an amplitude versus frequency Before proceeding on to a discussion of modulating a CW
plot of the individual waves which would have to be added RF carrier with a pulsed waveform, let's define the terms
together to produce the waveform. Since all the waves are used to represent the characteristics of a pulsed waveform.
integer multiples of the fundamental (PRF), the spacing
T
Fundamental Sum of Fundamental,
Average 2nd Harmonic and
Value of Average Value
Wave
2nd Harmonic
E
Epk
EAVG
TIME
Figure 1b. Addition of a fundamental cosine wave and its harmonics to Figure 3. Basic characteristics of a pulsed waveform
form rectangular pulses
Spectral Lines
y = sin x
x
Amplitude
1
T
DC