Modulators are circuits which varies the characteristics of output
signal according to the changes of the input signal properties. The
output and input signal properties includes amplitude, phase or
frequency.
A reactance modulator is a modulator circuit that
uses BJT or FET whose reactance is varied according to the input
modulating signal amplitude. In other words, the BJT or FET is operated
as voltage controlled capacitor or inductor whose capacitance or
inductance varies with applied modulating signal amplitude. When such
voltage controlled BJT or FET capacitor or inductor is connected to an
LC tank or oscillator then the frequency of the tank circuit or
oscillator changes in accordance with the modulating signal magnitude.
The reactance BJT or FET along with the LC tank or oscillator is called
reactance modulator.
The reactance of the BJT or the FET can be made either inductive or capacitive. The value of the reactance depends upon the transconductance of BJT or FET. The BJT or FET transconductance is in turn controlled using the biasing of the BJT base or FET gate. Reactance modulators are used along with various types of oscillator like Colpitts oscillator, Hartley oscillator, crystal oscillator to generate FM(Frequency Modulation) signals.
Shown below is a BJT based reactance modulator circuit diagram.
In the above BJT reactance modulator circuit diagram, the Q1 transistor transconductance controls the reactance which is connected across the LC tank(L1 and C1). The reactance modulator changes its reactance when the modulating signal V1 is applied. The change in reactance cause the frequency of the LC tank to change. The signal frequency of the LC tank is the carrier signal frequency. Hence the modulating signal modulates the frequency of the carrier signal and FM signal is generated.
The modulator reactance here is due to the capacitor C. The reactance Xc of this capacitor must be 5 to 10 times higher than the resistance R1. When this condition is met then the modulator reactance is capacitive. Thus the biasing of the BJT controls the reactance of the modulator. Another condition for making sure that the BJT circuit acts as a reactance modulator is that the current into the base of the transistor should be much smaller than the current flowing through the capacitor C and resistor R.
In the same circuit diagram below, let the current through the capacitor and resistor be Io, Ic is the collector, V is the voltage across the output of the BJT modulator and Z is the impedance.
The base voltage at the junction of the C and R is,
\(V_B = I_o R\) ------------>(1)
The current \(I_o\) is,
\(I_o = \frac{V}{R-jX_c}\)
Hence the equation(1) becomes,
\(V_B = \frac{V}{R-jX_c} R\) ----------->(2)
If \(g_m\) is the transconductance then we have,
\(g_m = \frac{I_c}{V_B}\)
And so we can write,
\(I_c = g_m V_B\) ------------>(3)
And replacing \(V_B\) from equation (2) in (3),
\(I_c = g_m \frac{V}{R-jX_c} R\)
If \(X_c >> R\) then we can rewrite above equation,
\(I_c = g_m \frac{V}{-jX_c} R\)
or, \(I_c = g_m \frac{V}{-j\frac{1}{wC}} R\)
that is, \(I_c = j w g_m V C R\) ---------->(4)
The impedance of the BJT with the capacitor(C) and resistor(R) is,
\(Z = \frac{V}{I_c}\) -------->(5)
Hence using \(I_c\) from equation (4), we have,
\(Z = \frac{V}{ j w g_m V C R}\)
or, \(Z = \frac{1}{ j w g_m C R}\)
Let, \(C_{eq} = g_mCR\) ---------------->(6)
then we have,
\(Z = \frac{1}{ j w C_{eq}}\) -------------->(7)
As
can be seen from the equation(7) the impedance of the BJT with the
capacitor and resistor is capacitive reactance with value given
equivalent capacitance given by equation (6). We can calculate the
reactance, equivalent capacitance value also using the online reactance modulator calculator.
By connecting the reactance modulator across an oscillator or LC tank circuit we can then change the frequency of the carrier signal by the applying modulating signal to the reactance modulator.
When the amplitude of the modulating varies, the transconductance of the BJT modulator changes which changes the equivalent capacitance of the BJT reactance modulator and since the equivalent capacitor is connected to the oscillator the frequency of the oscillator changes.
The equivalent capacitance(\(C_{eq}\)) of the BJT reactance modulator is,
\(C_{eq} = g_m RC\)
But the transconductance(\(g_m\)) of the BJT is,
\(g_m = \frac{I_c}{V_B}\)
and so the equivalent capacitance(\(C_{eq}\)) is,
\(C_{eq} = \frac{I_c RC}{V_B}\) ---------------->(8)
The following shows a BJT reactance modulator circuit diagram connected to Colpitts oscillator to generate FM signal.
