Diode Charge Pump

AM-FM Demodulators

AM-FM Demodulators

Article : Ramon Vargas Patron - Lima Peru

Email :ramonvargas15353@gmail.com

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 V_{1} volts and a resistor R_{1} connected to ground (Fig.1.b). The switch stays in each position equal periods of time.

In Fig.1.a, C_{p} is responsible for pumping charge towards the output capacitor C_{r}, which_{ }acts as a reservoir. Operation of the circuit is as follows.

When the switch is in position "a" a pulse of height V_{1} is applied to C_{p}. The charge received by this capacitor is distributed
between C_{r} and resistor R_{r}. At the end of the pulse, C_{p} discharges through R_{1} and D_{1} (switch in position "b").
Diode D_{2} does not conduct (is an open circuit) on this interval. As a consequence, C_{r} discharges through R_{r}. 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 R_{r}.

In the steady state, charge conservation dictates that:

(1)Here, q_{1} is the charge received by C_{p} per pulse; q_{2} is the charge transferred to C_{r}, also per pulse (it restores the charge lost
by this capacitor in the preceding cycle) and q_{r} is the charge that diverts through R_{r} (fraction of q_{1} that doesn't reach C_{r}).

The voltage across C_{p} increases in an amount D
V_{p} due to q_{1}. We may write then:

(2)

Assuming ideal diodes (zero voltage drop when conducting):

where V_{o} is the instantaneous value of the output voltage.

Substituting the above relationship into eq.(2) yields:

(3)

The voltage across C_{r} increases by an amount D
V_{o} due to q_{2}. Accordingly, we may write:

(4)

If we assume D
V_{o }<< V_{o }, the output voltage may be considered to be approximately constant. C_{r}'s discharge current in each operating cycle can then be approximated by the constant current i = V_{o} / R_{r}. Charge q_{2} may be found integrating this current over one half cycle of the input signal. Thus:

Working out the value for D
V_{o} yields:

(5)

and:

(6)

T is the repetition period of the input pulses.

For D
V_{o} to be much smaller than V_{o}, the following restriction must hold:

or:

(7)

Being the output voltage V_{o} approximately constant, we may write:

(8)

Substituting eqs. (3), (6) and (8) into eq.(1):

Solving for V_{o} we obtain, with T = 1/f:

(9)

We must bear in mind that *f *is the pulse rate or number of pulses per second.

For there to exist linearity between V_{o} and *f*,* * it must be satisfied that:

or that:

(10)

Under these conditions:

(11)

Clearly, a linear relationship exists between V_{o} and the pulse rate *f *, and also between the output and the height V_{1 }of the input pulses. The output linearly follows any frequency or amplitude input changes. Hence, the DCP may act as an AM/FM demodulator.

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 V_{g} has an amplitude V_{1} and frequency *f*, then for the unloaded case the steady-state output voltage will be *v _{o}* = 2V

Upon connection of a resistive load R_{r} (Fig.2.b), the output voltage *v _{o}* will no longer be a pure DC value. It will consist of a DC component V

Let D
V_{o} be the peak-to-peak value of the ripple superimposed on V_{o}, and D
V_{p} that of the ripple component across C_{p}. If D
V_{o}<<V_{o}, then:

(12)

Charge conservation throughout one cycle of the input signal dictates now that:

Thus:

V_{o} will be given by the expression:

Solving for V_{o} yields:

(13)

If we let that:

(14)

then:

(15)

which is the linear relationship we are looking for. Then, for an FM signal:

(16)

where D
V_{ofm} represents the output voltage variations following frequency changes D
*f* of the input.

For an AM signal:

(17)

Here, D
V_{oam} represents the output voltage variations following amplitude changes D
V_{1} 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:

or:

(18)

Summarizing:

Calculations have assumed ideal diodes, so corrections are needed to compensate for real world-diode voltage drops. For the no-modulation and FM cases, 2V_{1}-2V_{D} may be substituted for 2V_{1}, where V_{D} is the peak voltage drop in diodes D_{1} and D_{2} (assumed equal). Higher carrier amplitudes should help overcoming these voltage drops. However, provisions should be made to protect diodes from excessive peak currents.

Conducted measurements

The circuit depicted in Fig.3 was used for the FM demodulation tests. With the selected values for C_{p}, C_{r} and R_{r}, 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: V_{o} = 100mV DC

-FM modulated carrier with D*f* = +/-75kHz (calibration not checked) at a 1kHz rate:

D
V_{ofm} = 0.4mV peak

-AM modulated carrier at 30% with 1kHz, D
V_{1} = 0.3V peak: D
V_{oam }= 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 31^{st}, 2005