A phase-locked loop (PLL) angular modulator scheme has been proposed which has the characteristics of wideband modulation frequency response. The modulator design is independent of the PLL closed-loop transfer function H(s), thereby allowing independent optimization of the loop's parameters as well as the modulator's parameters. A phase modulator implementing the proposed scheme was built to phase modulate a low-noise phase-locked signal source at the output frequency of 2290 MHz. The measurement results validated the analysis by demonstrating that the resulting baseband modulation bandwidth exceeded that of the phase-locked loop by over an order of magnitude. However, it is expected to be able to achieve much wider response still

Nguyen, L.

English

NASA Technical Reports Server

'
'u
TDA Progress Report 42-98
N90-12798
August 15, 1989
Wideband Phase-Locked Angular Modulator
L. Nguyen
Radio Frequency and MicrowaveSubsystemsSection
A phase-locked loop (PLL) angular modulator scheme has been proposed which
has the characteristics of wideband modulation frequency response. The modulator
design is independent of the PLL closed-loop transfer function H(s), thereby allow-
ing independent optimization of the loop's parameters as well as the modulator's
parameters. A phase modulator implementing the proposed scheme was built to
phase modulate a low-noise phase-locked signal source at the output frequency of
2290 MHz. The measurement results validated the analysis by demonstrating that
the resulting baseband modulation bandwidth exceeded that of the phase-locked
loop by over an order of magnitude. However, it is expected to be able to achieve
much wider response still.
I. Introduction
Phase-locked loops (PLL) are sometimes designed to
mechanize the generation of phase modulation (PM) or
frequency modulation (FM) signals. In a synthesized sig-
nal generator, the same frequency synthesis loops are often
also used for providing PM and/or FM capability. As such
an angular modulator, the PLL has the following desirable
characteristics: the modulated carrier frequency can be
stabilized by a stable reference signal; and a large modu-
lation index can be obtained by suitable phase compression
in the loop [1]. In a typical phase-locked angular modula-
tor, shown in Fig. 1, the modulating signal is added to the
appropriate baseband points in the loop to produce the
desired PM or FM [2]. An analysis of this scheme shows
that the modulation transfer function relating the output
phase to the input phase modulating voltage is propor-
tional to the PLL closed-loop transfer function H(s) (a
low-pass function), whereas the function relating the out-
put instantaneous frequency to the input frequency modu-
lating voltage is proportional to the complementary high-
pass of H(s). This dependence of the modulation transfer
function on the PLL closed-loop characteristics has the
following consequences:
(1) The configuration of Fig. 1 does not lend itself to
easy implementation of both PM and FM using
the same loop. For PM, a sufficiently wide loop
bandwidth is required to accommodate the high
frequency modulating signal, whereas for FM a
narrowband loop is needed to prevent the loop
from tracking out the low frequency modulating
signal.
150
https://ntrs.nasa.gov/search.jsp?R=19900003482 2020-03-19T23:46:26+00:00Z
(2) Wideband modulation frequency response is of-
ten not possible since the design is usually con-
strained by considerations such as spurious signal
rejection, loop stability, settling time, and noise
performance that place upper and lower limits on
the loop bandwidth.
(3) The loop introduces phase distortion to the out-
put modulating envelope because of its band-
limited nature.
A phase-locked modulator scheme is proposed that
eliminates the above limitations. It will be shown that the
modulation transfer function resulting from this scheme,
which has the characteristics of wideband frequency re-
sponse, is independent of the PLL transfer function. An
experimental phase modulator was built. The measured
data substantiate the analysis by demonstrating that the
resulting baseband modulation bandwidth exceeded that
of the PLL by over an order of magnitude.
Simplifying yields
O0(s)= KoKDF(s)
s + KoKDF(S)On(s)
+ KoP(s) VM(S)
s + KoKDF(s)
KoF(s)Q(s)+ vM(s) (2)
s + KoKDF(S)
The quantity KoKDF(s)/[s + KoKDF(S)] is the closed-
loop transfer function, denoted H(s). Thus,
Oo(s) = H(s)OR(s) + KoP(s)
s + KoKDF(s)
v (s)
KoF(s)Q(s)
+ VM(s) (3)
s + KoKDF(s)
II. Analysis
Figure 2 shows the generalized block diagram of the
proposed modulator scheme. A noise-free and linearized
model of a PLL consisting of a phase detector, loop filter,
and a voltage-controlled oscillator (VCO) is assumed. The
following notation will be used:
On(s) = reference phase, rad
O0(s) = output phase, rad
OM(S) = output phase modulation, tad
OM(S) = output frequency modulation,
rad/sec
KD = phase detector gain, volt/tad
K0 = VCOs gain constant, rad/sec/volt
F(s) = loop filter
P(s), Q(s) = modulation filters
VM(S) = input modulating signal, volt
The output phase for the loop in Fig. 2 is given by
O0(s) -- -_-{P(s)VM(s)"4-F(s)[Q(s)VM(s)
(1)
OR(s) defines the reference phase for the loop to maintain
lock and is constant as far as the modulation is concerned.
So, the output phase modulation due to the input modu-
lating signal is
KoP(s)
OM(S) -- s + KoKDF(S) VM(S)
KoF(s)Q(s)
+ VM(s) (4)
which can be rearranged to yield
s KoKD P(s) VM(S)
OM(S) = s + KoKDF(s) s KD
KoKDF(s) ..., , VM(S) (5)
or
OM(S, = ([1-- ,(s)] K°--Ks_P(s)+H(s)O(s )} VM(S)KD
(6)
The output instantaneous frequency is the derivative
of the phase. Hence the output frequency modulation is
151
9M(,) = ,eM(,)
= {[1- H(s)]P(s)+ H(S)K-- KDQ(S)}KoVM(s)
(7)
It is evident from Eqs. (6) and (7) that the design
strategy is to choose the correct modulation filters P(s)
and Q(s) that would enable the appropriate compensa-
tions to eliminate the terms involving H(s) and thus allow
the modulation response to be independent of the PLL
transfer function parameters. That is, it is desirable to
choose P(s) and Q(s) such that the sums inside the brack-
ets of Eqs. i6) and (7) simplify to unity. The two cases of
PM and FM are considered.
A. Phase Modulation
Choose P(s) = s/KoKD. This is the transfer function
of a differentiator where the time constant equals 1/KoKD,
and choose Q(s) = 1. Then Eq. (6) becomes
oM(,) = {[1 - H(s)] KoKD ss KoKD + H(s)} VM(S) (8)
or
1
e_,(s) = #-_VM(s) (9)
The output phase is thus proportional to the input
modulating signal, scaled by the constant 1/KD. This is
the desired result.
B. Frequency Modulation
Choose P(s) = 1, and choose Q(s) = KoKD/s. This
is the transfer function of an integrator with the time con-
stant equal to 1/KoKD. Then, Eq. (7) becomes
s
tiM(S) = {[1 -- H(s)] + H(S)-KoKD KoKD }KoVM (s)S
(10)
or
tiM(S) = KoVM(s) (11)
The output instantaneous frequency is thus propor-
tional to the input modulating signal, scaled by the con-
stant K0. This is the desired result.
III. Discussion
Equations (9) and (11) demonstrate that the output
PM and FM frequency responses are independent of the
PLL transfer function His ). Specifically, the detail of the
loop filter Fis ) is completely irrelevant as far as the over-
all modulation process is concerned. To the extent that
the linearized model of the PLL is valid, and to the de-
gree that P(s) and Q(s) can be realized, the design of the
modulator can be completely independent from the PLL
closed-loop characteristics; the important parameters, as
shown by the analysis, are the phase detector and the VCO
gain constants. This independence of the modulation fre-
quency response from the transfer function His ) is ex-
tremely desirable. Since Eqs. (9) and ill) are implied, the
proposed modulator scheme is a wideband configuration
and therefore does not suffer from the inherent limitations
associated with the configuration of Fig. 1 as mentioned
above.
It is possible to obtain wideband response in the con-
figuration of Fig. 1 by introducing the appropriate com-
pensation networks to the input modulating signal prior
to the PLL modulation terminals and external to the PLL.
These networks would be in the form of 1/H(s) or 1/[1 -
His)] for PM or FM, respectively. The drawback is that
H(s) must be accurately known. Also, if a high-order loop
is required, the resulting high-order compensation network
could be difficult to design. Furthermore, the loop would
invariably have spurious poles contributed by the loop fil-
ter network. This would make extremely difficult the task
of fully characterizing His ) to the degree required for wide-
band compensation.
Based on the results of Eqs. (9) and (11) it is pos-
sible to propose an entirely new modulator configuration
which is shown in Fig. 2. This scheme takes advantage
of the feedback loop and applies the modulation to both
baseband positions before and after the loop filter such
that the modulator design is free from the effect and con-
straint of F(s). The compensation networks are simply
the differentiator and the integrator whose time constants
are solely determined by the product KoKD. They re-
main unchanged regardless of the specific detail of F(s),
and hence the loop order. In particular, as far as the mod-
ulator design is concerned, any spurious poles of F(s) or
of any networks in the signal path from the phase detector
output to the VCO input are lumped together with F(s)
as part of an equivalent loop filter. This also applies to
any time delay functions in that path. However, as will be
shown in the experimental results discussed in Section IV,
the design is not free of the effect of spurious poles in the
loop that are not made part of the loop filter.
152
This scheme is ideal since H(s) is self-negating to
unity as shown by Eqs. (8) and (10) and obviates the
necessity for an accurate external loop compensation to
tt(s) or the need to compromise between the PLL and the
modulator performance.
Figures 3 and 4 show block diagrams of the proposed
phase modulator and frequency modulator. It is evident
from the diagrams that the frequency modulator can be de-
rived from the phase modulator by inserting one integrator
in each of the phase-modulating signal-injection arms (one
of which nullifies the differentiator).
The linearity requirement constrains the peak modu-
lation index seen at the phase detector, hereafter denoted
/_p. This means that the sum of the peak phase error in the
absence of modulation and /_p must be within the linear
range of the phase detector. For a sinusoidal phase detec-
tor transfer function, this sum should not exceed 30 deg
for good linearity. Also, since the PLL is a carrier tracking
loop, the design must prevent the range of modulation in-
dex from causing a carrier-null at the phase detector input.
The constraint on/_p can be mitigated by judicious choice
of the phase compression factor N in the feedback loop
that would permit a broader range of modulation index at
the loop output.
Linearity of the integrator and the differentiator also
constrains _p. In the PM case, it can be shown that /_p
must satisfy/_p < KoVsAT/(2_rf, na_), where VSA T is the
saturation voltage of the differentiator and fmax is the
highest input modulating frequency. Similarly in the FM
case, /_p must satisfy/_p < VSAT/KD, where VSAT is the
saturation voltage of the integrator (here /?p is the ratio
of the maximum frequency deviation and the lowest input
modulating frequency).
It would appear from Eq. (11) for the FM case that
it would be possible to apply modulation at very low fre-
quency all the way down to DC. Then, one could generate
a constant frequency shift at the VCO output by applying
a constant DC voltage at the modulating input. However,
a DC response is not possible in reality because the inte-
grator (in Fig. 4) would eventually saturate. Secondly, the
phase error would eventually exceed the dynamic range
of the phase detector and the loop would then no longer
remain linear or in lock. However, by careful design to pre-
vent component saturation and to remain within the linear
range of the PLL, it is possible to modulate the frequency
as close to DC as desired.
IV. Experiments
A phase modulator implementing the proposed
scheme was built to verify the analysis. It was designed
to phase modulate a phase-locked signal source whose de-
sign emphasis is for phase-noise and spurious signal power
spectral density performance. A block diagram of the cir-
cuit is shown in Fig. 5. Basically, the loop is a second-
order PLL and is of the mix-down-and-divide design for
low-noise performance. The VCO is a cavity oscillator
operating at a frequency of 2290 MHz. The x24 mul-
tiplies the 95-MHz phase-locked crystal oscillator output
frequency to 2280 MHz. The 2280-MHz signal downcon-
verts the cavity oscillator output at 2290 MHz to an IF
of 10 MHz. The +2,frequency divides the 10-MHz IF to
5 MHz and effects a phase compression by a factor of 2.
A temperature-stabilized low-noise crystal oscillator pro-
vides the 5-MHz reference signal. From the phase-noise
data of the 95-MHz phase-locked crystal oscillator and the
free-running cavity oscillator, the loop parameters were
designed for optimum phase noise performance at the out-
put, with the constraint of adequate rejection of the 5-MHz
reference signal feed-through. The loop natural frequency
was selected to be about 35 kHz and the damping ratio to
be 0.707. Measured gain constants of the sinusoid phase
detector and the VCO are 0.30 volt/rad and 300 kHz/volt,
respectively, which yields the time constant 1/KoKD of
1.77 psec. An op-amp differentiator with a 3-dB band-
width of about 14 MHz was used. A gain adjustment was
included as part of the differentiator to effectively provide
the adjustment of the time constant.
To test the circuit, a baseband sinusoidal signal from
a signal generator was applied to phase modulate the 2290-
MHz carrier output. To assure linearity at the phase detec-
tor and not to exceed the linear range of the differentiator
at high modulation frequency, the modulation index was
kept small, at about 3 deg. The output was then observed
on a spectrum analyzer while sweeping the input modulat-
ing signal frequency. The spectrum analyzer thus displays
the magnitude of the modulation transfer function being
measured at the carrier frequency.
Figure 6 shows the result when the modulating sig-
nal is applied to the loop filter input only. As would be
expected, the output modulation spectrum is symmetri-
cal about the carrier frequency. Note that in this case
the display spectrum envelope is proportional to ]H(jw)[.
It can be seen that the actual natural frequency is about
40 kHz, and the damping ratio is about 0.50. The 3-dB
bandwidth of the loop is about 75 kHz. Figure 7 shows
the result when the modulating signal is applied to the
differentiator input only; here the spectrum envelope is
153
proportional to [1- H(jw)[. These two cases correspond
to the configuration in Fig. 1, and the results in Figs. 6
and 7 demonstrate the band-limited nature of that circuit.
Figure 8 shows the spectrum analyzer display when
the modulating signal is applied to both inputs of the
loop filter and the differentiator. Note that the previous
high- and low-frequency roll-offs in Figs. 6 and 7 as well
as the amplitude peakings occurring at the loop's natural
frequency have disappeared. The flat spectrum indicates
that wideband frequency response has been achieved as
predicted by the analysis. Figure 9 shows the same results
but with the spectrum analyzer set at a 10-MHz span. As
can be seen by comparing Figs. 6 and 8 (or 9), the phase
modulation transfer function bandwidth has increased by
more than an order of magnitude over that of the PLL.
Specifically, the baseband modulation 3-dB bandwidth as
shown in Fig. 9 is about 1.50 MHz in comparison with
the 3-dB bandwidth of only 75 kHz for the loop as shown
in Fig. 6. The rolling-off of the output modulation spec-
trum in Fig. 9 (instead of its remaining flat as it should)
was puzzling at first. It was later realized that this is
because the driving circuit of the VCO varactor diode as
seen from the output of the differentiator network approx-
imates an RC lowpass function with a 3-dB bandwidth of
about 1.50 MHz. This forms a spurious pole as discussed
in Section III. Suffice it to say that this part of the cir-
cuit must be designed properly or be lumped as part of
the loop filter network in order to improve high frequency
modulation performance.
V. Conclusion
A phase-locked angular modulator scheme has been
proposed which has the characteristics of wideband mod-
ulation frequency response. The modulator design is in-
dependent of the PLL closed-loop transfer function H(s),
thereby allowing independent optimization of the PLL pa-
rameters as well as the modulator's parameters. A phase
modulator implementing the proposed scheme was built to
phase modulate a phase-locked signal source that was de-
signed for low-noise performance at 2290 MHz. The mea-
surement results validated the analysis by demonstrating
that the resulting baseband modulation 3-dB bandwidth
exceeded that of the PLL by over an order of magnitude.
With an additional implementation effort and measure-
ments to improve the high frequency performance, it is
expected that flat wideband modulation response from DC
well into the MHz regions can be achieved.
Acknowledgment
The author expresses gratitude to Carl Johns and North Ham for the valuable
comments and discussions.
References
[1] G. R. Vaughan and E. Osborne, "Phase Locked Phase Modulator," IEEE In-
lernationai Communications Conference Record, Digest of Papers, New York,
pp. 206-207, 1966.
[2] F. M. Gardner, Phaselock Techniques, New York: John Wiley & Sons, 2nd
edition, 1979.
154
PHASE
MODULATING
I SIGNAL
PHASE I
REFERENCE t _ I
OSC,LLATO.J l
I I ........... l _ _ FREQUENCY
[_1 r,,_,_,y_._., I_ _ )'_ + /_m----MODULATING
I ...... I I _ _ SIGNALIOUTPUT
Fig. 1. Typical phase-locked modulator [2].
eR (s) +
O0(s)_
Fig. 2. Proposed phase-locked modulator.
,---VM(S)
_ oM _s_
Fig. 3. Proposed wideband phase modulator.
VM(s)
, VM(S)
Fig. 4. Proposed wideband frequency modulator.
95-MHz PHASE- 2290-MHz PHASE-
LOCKED OSCILLATOR MODULATED OUTPUT
/ ql I CAVITY VCO
_-_ 1 I l -I_ _...J - 22§0 MHz _ _ I
5-MHz I I -- Ko I
CRYSTAL I _ - I
OSCILLATOR _
SIGNALI l .I-'- _..I I
GENERATOR PHASE-MODULATING
S GNAL NPUT
Fig. 5. Experimental wideband phase modulator.
155
1 I I I I I I I
-- RL 16.00 dBM
AT'I'EN 30 dB
6.00 d B/DIV
1 I I I I I I I I
CENTER 2.289 997 GHz SPAN 1,00 MHz
RB 3.00 kHz VB 3.00 kHz ST 333.3 msec
Fig. 6. Output phase modulation spectrum without
compensating differentlator.
I I I I
RL 16.00 dBM
ATTEN 30 dB
6.00 dB/DIV
p..-- I
I I I I
B I
I I I I 1 I I 1 I
;ENTER 2.289 997 GHz SPAN 1.00 MHz
RB 3.00 kHz VB 3.00 kHz ST 333.3 msec
Fi 8. 8. Output phase modulation spectrum of the
proposed wldeband scheme.
I I I I
t-- RL 16.00 dBM
A'I-rEN 30 dB
6.00 dB/DIV
I I I I
I I I I I I I I I
',ENTER 2.289 997 GHz SPAN 1,00 MHz
RB 3,00 kHz VB 3.00 kHz ST 333.3 msec
Fig. 7. Output phase modulation spectrum with
compensating differentiator only.
1 I I I
RL 16.00 dBM
A'I-FEN 30 dB
6.00 dB/DIV
I I I I
I I I
CENTER 2.289 98 GHz
RB 3.00 kHz VB 30.0 kHz
I I J I I I
SPAN 10.00 MHz
ST 50.00 msec
Fig. 9. Output phase modulation spectrum of the
proposed wideband scheme at IO-MHz span.
156


Wideband phase-locked angular modulator

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server