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Agilent AN 1309
Pulsed Carrier Phase Noise
Measurements
Application Note
Agilent E5500 phase noise
measurement system
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
PRF Feedthrough
Minimum Duty Cycle
Summary
2
Chapter 1
Introduction absolute noise of individual oscillators but to know
Advances in RF and microwave communication the residual or additive noise of signal processing
technology have extended system performance to devices like power amplifiers and pulse modulators.
levels previously unattainable. Design emphasis on Because the final signal in most radar systems is
sensitivity and selectivity have resulted in dramatic pulsed, making absolute phase noise measurements
improvements in those areas. However, as factors on the pulsed carrier is essential to determining
previously limiting system performance have been the overall performance of the system.
overcome, new limitations arise and certain para-
meters take on increased importance. One of these This application note discusses basic fundamentals
parameters is the phase noise of signal sources for making pulsed carrier phase noise measurements.
used in pulsed RF and microwave systems.
The assumption is made that the reader is familiar
In pulsed radar systems, for example, the phase with the basic concepts of phase noise and CW
noise of the receiver local oscillator sets the mini- phase noise measurement techniques.
mum signal level that must be returned from a
target in order to be detectable. In this case, phase Chapter 2 reviews the fundamentals of pulsed
noise affects the selectivity of the radar receiver carriers in the frequency and time domains. The
which in turn determines the effective range of the majority of terms used in succeeding chapters are
overall system. defined throughout Chapter 2. Chapter 3 discusses
how the single sideband phase noise of a CW carrier
Since the overall dynamic range of the radar sys- is affected by the pulse modulation process. Chap-
tem is influenced by the noise of the transmitted ter 4 discusses the effects a pulsed RF carrier has
signal, it is not only important to know the on the performance of a phase detector based
measurement.
3
Chapter 2
Fundamentals of Pulsed Carriers the amplitudes of the higher order harmonics are
The formation of a square wave from a fundamen- relatively small, so reasonably shaped rectangular
tal sine wave and its odd harmonics is a good way waves can be produced with a limited number of
to begin a discussion of pulsed carriers and their harmonics. By changing the relative amplitudes
representation in the time and frequency domains. and phases of the harmonics, both odd and even,
an infinite number of waveshapes can be plotted.
You might recall having plotted a sine wave and
its odd harmonics on a sheet of graph paper, then To create a train of pulses (i.e., a waveform whose
adding up all the instantaneous values. If there amplitude alternates between zero and one) with a
were enough harmonics plotted at their correct series of sine waves, a dc component must be added.
amplitudes and phases, the resultant waveform Its value equals the amplitude of the negative loops
would begin to approach a square wave. The funda- of the rectangular wave with the sign reversed.
mental frequency determined the square wave
rate, and the amplitudes of the harmonics varied Consider a perfect rectangular pulse train as shown
inversely to their number. in Figure 1a, perfect in the sense that the rise time
is zero and there is no overshoot or other aberra-
A rectangular wave is merely an extension of this tions. This pulse is shown in the time domain and
principle. In fact, to produce a rectangular wave, if we wish to examine it in the frequency domain it
the phases must be such that all the harmonics must be broken down into its individual frequency
go through a positive or negative maximum at the components. Figure 1b superimposes the funda-
same time as the fundamental. Theoretically, to mental and its second harmonic plus a constant
produce a perfectly rectangular wave, an infinite voltage to show how the pulse begins to take shape
number of harmonics would be required. Actually, as more harmonics are plotted.
T
E
A
TIME
Figure 1a. Periodic rectangular pulse train
4
A spectrum analyzer would in effect "unplot" these to the PRF. The envelope of this plot follows a
waveforms and present the fundamental and each sinX/X function with the spectral line frequencies
harmonic 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
A frequency domain plot of this waveform would of the pulse width.
be as shown in Figure 2. This is an amplitude versus
frequency plot of the individual waves which would Before proceeding on to a discussion of modulating
have to be added together to produce the waveform. a CW RF carrier with a pulsed waveform, let's
Since all the waves are integer multiples of the fun- define the terms used to represent the character-
damental (PRF), the spacing between lines is equal istics of a pulsed waveform.
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 Figure 3. Basic characteristics of a pulsed waveform
harmonics to form rectangular pulses
Spectral Lines
y = sin x
x
Amplitude
1
T
DC
FREQUENCY, f
Figure 2. Spectrum of a perfectly rectangular pulse. Amplitudes and phases of
an infinite number of harmonics are plotted resulting in a smooth envelope as
shown.
5
Referring to Figure 3: With this background we can now apply the pulsed
waveform as amplitude modulation to a continuous
wave RF carrier. A pulsed carrier is typically a
continuous wave carrier whose amplitude is modu-
lated by a rectangular pulse train having a relative
amplitude of one during each pulse and zero dur-
ing the period between pulses. Pulsed carriers can
also be generated by pulsing a frequency generat-
ing device, such as an oscillator, on and off. One
of the fundamental differences between these two
methods is that an amplitude modulated CW carrier
is phase continuous from pulse to pulse, whereas
the phase of a frequency generating device, which
is pulsed on and off, is random. Most measurement
systems, using the phase detector technique, can
only measure the phase noise of phase continuous
signals. The phase detector technique requires that
the two input signals be at quadrature (i.e., 90
degrees out of phase). If quadrature is lost, the sys-
tem will terminate the measurement. Quadrature
cannot be maintained if the phase from pulse to
pulse is random.
pulse is on during one complete cycle.
6
From single tone AM modulation theory we know The spectral line frequencies can be expressed as:
that sidebands will be produced above and below
the carrier frequency. The concept is the same for FL = FC ◦ Jabse Service Manual Search 2026 ◦ Jabse Pravopis ◦ onTap.bg ◦ Other service manual resources online : Fixya ◦ eServiceinfo