Variable Frequency Oscillator Gain Limiting
The VFO is one of the main subsystems in a transceiver. It sets
the operating frequency for both reception and transmission. In
order to “tune” to other frequencies, we actually change the
frequency of this variable frequency oscillator.
Two general methods for making variable oscillators are:
1. Begin with a crystal oscillator and pass the signal through
dividing or multiplication circuits to create sinusoids at
other frequencies. This is called a synthesized source (like
your Agilent 33120A).
2. Using an LC oscillator with a variable C and/or L.
Synthesized sources often are very stable wrt temperature and
other climate effects. However, these circuits are generally
complex and expensive.
LC oscillators are often cheaper but can be less stable with
temperature, humidity and other environmental changes. Our
VFO uses a varactor in an LC oscillator to tune frequency.
It is important that once a frequency is set for communication,
the transceiver frequency should not vary (at least not too
much). Frequency Drift
In the NorCal 40A, the VFO operates at 2.1 MHz and is used as
an input to the Transmit and RF Mixers

One reason for choosing a relatively “low” VFO frequency is
that frequency drift is proportional to operating frequency.
Hence, a lower f produces a smaller f drift per ºC change.
Also, note that the VFO circuitry in the NorCal 40A is
physically as far away as possible from the Power Amplifier.
The PA generates most of the heat in the transceiver.
The temperature coefficient ? of some quantity x is defined as

where T is the temperature (usually ºC).
Your text lists temperature coefficients for many NorCal 40A
components in Tables D.1 and D.2 on p. 356. (You can also find
these coefficients in component data sheets.)
For example:
• T68-7 core (for L9) has ? = +50 ppm/ºC,
• Polystyrene capacitors (C51-C53) have ? = ?150 ppm/ºC.
Note that ppm = parts per million = Hz/MHz for our purposes.
These four components in the VFO have oppositely signed
temperature coefficients! Consequently, these two competing
effects help to reduce the frequency drift caused by temperature
changes . Plus, polystyrene capacitors are largely immune to humidity changes. Apparatus for Problems 27 and 29
In Prob. 27, you will measure the temperature coefficient ? for
your VFO, and make an estimate of the expected value.
An apparatus has been constructed to enclose your PCB when
making these ? measurements. Warm your PCB with the heat
gun through the holes on the sides of the container. Be careful
not to melt the plastic container. To help with this, hold the heat
gun back about 1 foot and wave it back and forth.

Gain Limiting
The VFO in the NorCal 40A is a Clapp oscillator, as shown in
Fig. 11.4 and discussed in the last lecture. However, it turns out
that the JFET amplifier is not overloaded, as sketched in order to obtain the gain condition |G |= |L |for oscillation.
Instead, there is special gain limiting circuitry that has been
added to the VFO to keep the JFET from overloading, but still
allows the gain to vary with power level. This gain limiting circuit is formed from the diode, startup resistor and the divider capacitors C_{1} and C_{2} shown in

The purpose of the additional components are:
• Startup resistor (R21 = 47 k?): When the NorCal 40A is
turned on, R21 ensures that the initial gate voltage is zero.
This provides a large g_{m} so that the oscillator starts easily [g_{m} > 1/R ].
• Choke (RFC2 = 1 mH): This forces the DC value of the
output voltage V_{s} equal to zero.
• Gain limiting diode (D9 = 1N4148): This diode only
conducts for short periods of time when the sinusoidal gate
voltage V_{g} is near positive peaks.
Considering this last component more carefully, when D9
conducts, current flows up through the divider caps C_{1} and C_{2},
and then down through D. Consequently, charge is pulled from
the caps leaving them with a net charge per cycle. This provides
a negative dc voltage on the gate:

The caps will discharge through the startup resistor, but that
time constant ? is much greater than T (=1/f = 1/2.1 MHz). Gain Limiting Circuit Simulation
The gain of the JFET amplifier Q8 in the VFO is limited by the
circuit shown in Fig. 11.6. In a simulation of the VFO circuit
here, we’re going to use the It Sine transient current source in
ADS, which is zero for t < 0 and a sinusoid for t > 0. This
current source does not appear in the Nor Cal 40A VFO, and is
used here only to illustrate how the capacitors C52 and C53 are
charged up for gain limiting purposes.

The intended operation of this gain limiting circuit is for the
ideal diode DIODE1 to conduct only for positive peaks in I1.
The capacitors slowly charge up and over many periods of the
current source reach a steady negative voltage, which is
precisely what is needed to limit the gain of Q8. In the following result, we can see that the voltage across the two capacitors indeed becomes negative and constant with time:

Here are measurements from the actual VFO in the NorCal 40A:

The yellow trace is the source voltage of Q8, while the blue
trace is the gate voltage. Note that this latter voltage has a
negative average value, as predicted. Operation of the Gain Limiting VFO Circuit
1. As long as g_{m} > 1/R, the oscillation grows.
2. As the diode conducts current, it pulls charge through C1 and
C2 thus reducing V_{g} (< 0) further.
3. As V_{gs} becomes more negative, g_{m} decreases, as shown in

4. Eventually equilibrium is reached when the oscillation
conditions |G| =|L| and ?G = ?L are satisfied. In this state,
the output voltage oscillates and neither increases in
amplitude nor decreases. VFO Large Signal Analysis
The steady-state JFET source and gate voltages are sketched in
above. This can be directly compared with the oscilloscope screen shot shown on page 7. As shown in the text, the large-signal oscillation condition is

where G_{m} is the large-signal transconductance of the JFET amplifier. It is defined as

where I_{d.pp} and V_{gs.pp} are peak-to-peak values of the fundamental components (i.e., Fourier terms with frequency = 1?? ) of the drain current and the gate-to-source voltage, respectively. Our task now is to compute the p-t-p values of these fundamental frequency components so we can determine G_{m}. In our VFO, C_{1} = C_{2} so that from V_{g} 2V_{s} Because of the choke, V_{s} has zero dc value, whereas V_{g} has a dc value of V_{b} (< 0) due to the gain limiting circuit.It turns out that V_{b} is smaller than the pinch off voltage V_{c} of the JFET, as shown in

Consequently, this amplifier is operated in class C! The
transistor is either on or off. If we approximate V_{gs} as

then during the “on” times of the JFET

It is this cosine-squared shape that is sketched above in
The dc value of the drain current Io in the VFO JFET is

Or

As shown in Section B.4 from a Fourier series expansion of a
cosine square function, the p-t-p amplitude of the fundamental
component is four times the dc value:
I_{dpp} = 4? I_{0} ? I_{m}
In words, (11.38) means that the p-t-p fundamental current
component (i.e., a 2.1-MHz sinusoidal current) of the VFO
JFET drain current, I_{dpp}, is simply equal to I_{m}. Now, we divide (11.38) by _{spp} which is the p-t-p output (i.e., JFET source) voltage and find

contains a plot of (apparently) I_{dss} and V_{c} for some particular JFET:

In Prob. 27.B you will use to predict V_{s pp} for a particular load resistance (since G_{m} = 1/R). (I didn’t obtain very good results for this part.)