The tuned circuit or LC phase modulator is one of several methods used to generate phase
modulation for communications transmitters. Although the general aspects on the workings
of the LC phase modulator have been described in many articles and textbooks, the
operation of the modulator, with respect to the distortion and the effects of the voltage
variable capacitor, is not well documented in current literature.

In Summary:

This paper shows that the main distortion product from an LC phase modulator is from the
nonlinear phase shift curve of a resonant circuit and not from the varicap used to modulate
the circuit.

The operation of an LC phase modulator:

There are various designs of phase modulators that are referred to as reactance modulators
and the LC phase modulator is one form of a reactance modulator. The LC modulator is a
circuit that is resonant at the frequency that is to be phase modulated. The circuit can be a
parallel or series resonant circuit, however the series circuit is the most common. Whether
the circuit is parallel or series, the operation principle is the same.

Inductor
R
Voltage Variable
C a p a c i t o r
R F I n p u t
B i a s V o l t a g e ( V b ) + M o d u l a t i o n I n p u t ( V m )
P h a s e M o d u l a t e d
R F O u t p u t
S implified Circuit for an LC Phase M o d u lator


Figure 1.

In the simplified circuit for an LC phase modulator, the value of the inductor and the
capacitor are selected to be resonant at the frequency of the RF input. The resistor value sets
the Q or bandwidth of the circuit. Since inductors have finite Q, the resistor also includes
the resistance of the inductor.


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The voltage variable capacitor is commonly known as a varactor or varicap diode. The bias
voltage (Vb) sets the desired capacitance to be resonant at the RF input frequency with the
inductor. When the modulation voltage (which is summed with the bias voltage) is applied,
the resonant frequency of the circuit varies above and below the center frequency at the
modulation voltage magnitude.



Figure 2.

Figure 2 shows the amplitude and phase of a single tuned resonant circuit. The plot is
normalized so units are independent of Q. The plot shows the phase shift of 45 degrees
(0.785 radians) at the 3 dB points on the amplitude curve. The curve for phase is a tangent
curve and goes from +90 to 90 degrees with zero degrees at resonance. The modulation of
the voltage to the varicap shifting the resonant frequency results in phase shifting the output
following the phase response curve.

Simulation and Measurement of the LC phase modulator:

The simulation to determine the theoretical distortion for a LC phase modulator was to
apply a sine wave to a tangent function block and then measure the distortion after it passes
through the tangent function block with an FFT for the %THD. This is essentially a
mathematical model of the phase modulator.
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The measurement of a real LC phase modulator proved to be more difficult as the amount
of delta frequency (100 Hz) at a typical channel element frequency was very small. This
required building an FM discriminator with high sensitivity and low noise for the
measurements. Even with a very good PLL PM discriminator, the distortion measurements
were made with a spectrum analyzer (HP3580A) to measure the distortion components
relative to the fundamental because of the broadband noise floor.

The circuit was essentially the simplified circuit of figure 1 with an RF signal generator
driving the input and the output connected to the 50 ohm input of the FM discriminator.
The frequency used was 11 MHz.

Measurements were made with two different Qs ( 10 and 30 ) and two different diodes:
( MV209 and the GE varicap ).

LC Phase Modulator Distortion
0
1
2
3
4
5
6
7
8
9
10
11
12
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radians
% Distortion
Simulation
Measured

Figure 3.

There was not a significant difference between the four measurement results, so only one
curve is shown for the measured distortion. It was expected that Q would not be a factor in
the distortion, but it was unexpected that the varicap was not a contributor to the distortion.
In fact the varicap actually makes the distortion lower past about 0.7 radians. Contrary to
popular belief, the varicap is not the element causing the distortion. Instead, the distortion is
predictable and is due to the nonlinear phase shift of the tan x function. Figure 3 is a
comparison of calculated or simulated results with measured results (de-emphasis output).



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FM Discriminator output results:

The distortion results in figure 3 were measured at the de-emphasis output of the FM
discriminator because the output at the FM discriminator has a 6 dB per octave rising
response and as a result, the distortion would be higher than the phase modulated input.

LC Phase Modulator Distortion
0
5
10
15
20
25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radians
% Distortion
Measured De-emphasis
Measured - FM Discriminator

Figure 4.



The dominant distortion product from the LC phase modulator is the third harmonic. The
rising response of the FM discriminator then causes the third harmonic to be a factor of 3 or
10 dB higher relative to the fundamental then it would be after de-emphasis to restore the
modulation of the phase modulated signal. Figure 4 shows the factor of 3 higher distortion
at the FM discriminator output relative to the integrated or de-emphasis output.





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Distortion relative to the transmitter output:

So far, the distortion has been presented in the phase modulator terms, that is, delta phase
shift in radians. Normally transmitters are specified in terms of delta frequency shift
(deviation) in Hertz. In angle modulation transmitters (FM or PM modulators) the unit that
connects them is the modulation index (Note: Frequency and phase modulation occur
simultaneously together and each represent a different aspect of the same thing, angle
modulation). It follows that the modulation index = delta-phase (radians) = delta-frequency
(Hertz) (deviation) / modulating frequency. Thus the relationship between the two is the
modulating frequency. For example, if the deviation is known, then divide the deviation by
the modulating frequency for phase shift in radians. If this is for the transmitter output, then
divide the result by the transmitter multiplier number for the phase shift in radians at the
modulator.

For example, the GE 450 MHz exciter has a X36 multiplier, so for the distortion of this
exciter at 5 KHz deviation and a 1KHz modulating frequency (modulation index = 5) ( 5
radians / 36 = 0.14 radians) would be about 0.2% assuming no other contributions to the
distortion other than the phase modulator itself.

GE 450 MHz Exciter measurement results:

Before distortion measurements were made on the exciter, careful adjustment of the LC
modulator and the first two multiplier stages were made for minimum distortion. It was
found that these adjustments greatly affected the distortion. A spectrum analyzer connected
to the FM discriminator was used to make the adjustments. During the adjustments, it was
found that a second harmonic component was also present which set the lowest level of
distortion for the exciter.

The measurements were made by connecting an audio generator to the microphone input
and adjusting the output level for 4 KHz of deviation at all the test frequencies. This
simulates a typical voice spectrum input to the modulator. The deviation level was set to max
to insure that the audio limiter was not creating any distortion also the measurements were
done at the CG input with the same results.


Modulation
Frequency
Delta Radians at
RF Output
Delta Radians at
LC Modulator
Simulated
% Distortion
3
rd
Harmonic
Measured
% Distortion
THD HP333A
200 Hz
20.0
0.56
2.8
2.24
300 Hz
12.6
0.35
1.0
1.0
500 Hz
8.0
0.22
0.4
0.4
1000 Hz
4.0
0.11
0.1
0.4
2000 Hz
2.0
0.056
0.05
0.4
3000 Hz
1.3
0.036
0.04
0.4
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As noted in the adjustment phase, the second harmonic kept the distortion from going lower
as would be expected at 1000 Hz and above.

Since the distortion after adjustment is a reasonable number, the most significant step in
lowering distortion of a GE exciter is to adjust the modulator and the first and second
multipliers for lowest distortion. I accomplished the adjustment using my FM discriminator
and a HP3580A audio spectrum analyzer.

Conclusion:

The distortion data presented can now be used to determine what the distortion level will be