Frequency-to-voltage converters form part of a wide variety of instrumentation circuits. They also find use in radio as FM demodulators. One interesting configuration for this application is the Diode Charge Pump circuit (DCP), which also doubles as an AM detector.
The DCP is basically a pulse-driven half-wave voltage doubler. Its use as a demodulator derives from the analysis of charge transfer taking place between circuit components.
In this article I will attempt to explain why the demodulation process takes place in the DCP. Following, the circuit will be studied under AC sine-wave excitation.
Let's begin then analysing a voltage doubler driven by a periodic train of single-polarity pulses having a duty cycle of 50% (Fig.1.a). We shall model this situation by a switch that toggles between a battery delivering V1 volts and a resistor R1 connected to ground (Fig.1.b). The switch stays in each position equal periods of time.
In Fig.1.a, Cp is responsible for pumping charge towards the output capacitor Cr, which acts as a reservoir. Operation of the circuit is as follows.
When the switch is in position "a" a pulse of height V1 is applied to Cp. The charge received by this capacitor is distributed between Cr and resistor Rr. At the end of the pulse, Cp discharges through R1 and D1 (switch in position "b"). Diode D2 does not conduct (is an open circuit) on this interval. As a consequence, Cr discharges through Rr. When the switch returns to the "a" position, the operation cycle is repeated. If the pulse rate is sufficiently high, Cr's discharge will be incomplete on each cycle and a continuous current will flow through Rr.
In the steady state, charge conservation dictates that:(1)
Here, q1 is the charge received by Cp per pulse; q2 is the charge transferred to Cr, also per pulse (it restores the charge lost by this capacitor in the preceding cycle) and qr is the charge that diverts through Rr (fraction of q1 that doesn't reach Cr).
The voltage across Cp increases in an amount D Vp due to q1. We may write then:
Assuming ideal diodes (zero voltage drop when conducting):
where Vo is the instantaneous value of the output voltage.
Substituting the above relationship into eq.(2) yields:
The voltage across Cr increases by an amount D Vo due to q2. Accordingly, we may write:
If we assume D Vo << Vo , the output voltage may be considered to be approximately constant. Cr's discharge current in each operating cycle can then be approximated by the constant current i = Vo / Rr. Charge q2 may be found integrating this current over one half cycle of the input signal. Thus:
Working out the value for D Vo yields:
T is the repetition period of the input pulses.
For D Vo to be much smaller than Vo, the following restriction must hold:
Being the output voltage Vo approximately constant, we may write:
Substituting eqs. (3), (6) and (8) into eq.(1):
Solving for Vo we obtain, with T = 1/f:
We must bear in mind that f is the pulse rate or number of pulses per second.
For there to exist linearity between Vo and f, it must be satisfied that:
Under these conditions:
Clearly, a linear relationship exists between Vo and the pulse rate f , and also between the output and the height V1 of the input pulses. The output linearly follows any frequency or amplitude input changes. Hence, the DCP may act as an AM/FM demodulator.Sine-wave excitation analysis
The DCP was subjected to tests with AM and FM modulated AC sine-wave inputs. In each case, successful recovery of the modulating signal could be achieved. It has then been found advisable to analyse the demodulation process with these new input conditions.
Sine excitation suggests that it is best to look at the circuit as being a half-wave voltage doubler. With this in mind, if the source voltage Vg has an amplitude V1 and frequency f, then for the unloaded case the steady-state output voltage will be vo = 2V1. Note that capacitor Cp will be charged to V1 volts (Fig.2.a).
Upon connection of a resistive load Rr (Fig.2.b), the output voltage vo will no longer be a pure DC value. It will consist of a DC component Vo and some ripple superimposed on it. D2 will conduct for a brief time in the neighborhood of the positive peaks of Vg, transferring charge from Cp to Cr. This last capacitor discharges across Rr when D2 is off, which occurs during most of the time interval between positive peaks of the input voltage. Cp replenishes its charge when D1 briefly conducts in the neighborhood of the negative peaks of Vg. As a result of these actions vo will have some ripple added, as stated before, and also will the voltage across Cp.
Let D Vo be the peak-to-peak value of the ripple superimposed on Vo, and D Vp that of the ripple component across Cp. If D Vo<<Vo, then:
Charge conservation throughout one cycle of the input signal dictates now that:
Vo will be given by the expression:
Solving for Vo yields:
If we let that:
which is the linear relationship we are looking for. Then, for an FM signal:
where D Vofm represents the output voltage variations following frequency changes D f of the input.
For an AM signal:
Here, D Voam represents the output voltage variations following amplitude changes D V1 of the input signal. Thus, the output linearly follows the modulating signal.
It is desirable that the ripple at the unmodulated input frequency be much smaller than the DC output. Then, the following must also be satisfied:
Calculations have assumed ideal diodes, so corrections are needed to compensate for real world-diode voltage drops. For the no-modulation and FM cases, 2V1-2VD may be substituted for 2V1, where VD is the peak voltage drop in diodes D1 and D2 (assumed equal). Higher carrier amplitudes should help overcoming these voltage drops. However, provisions should be made to protect diodes from excessive peak currents.
The circuit depicted in Fig.3 was used for the FM demodulation tests. With the selected values for Cp, Cr and Rr, the following figures were obtained:
(regretfully, not much greater than 1) and:
A Hewlett-Packard 8601A Sweeper Generator was used as the signal source for a 1-Volt amplitude 10.7MHz carrier, and accordingly, the following values were obtained at the input of the two-transistor amplifier stage:
-No modulation: Vo = 100mV DC
-FM modulated carrier with Df = +/-75kHz (calibration not checked) at a 1kHz rate:
D Vofm = 0.4mV peak
-AM modulated carrier at 30% with 1kHz, D V1 = 0.3V peak: D Voam = 40mV peak
Amplification was used in the FM case for easy viewing of the recovered modulation.
Fig.3 Circuit used for testing FM demodulation with the DCP
Ramon Vargas Patron
Lima-Peru, South America
January 31st, 2005