Stable RF oscillation
Optocoupler-based negative differential-resistance

by Ofer Aluf, MSc (Physics), Optoelectronics Technical Specialist, Future Electronics (Israel)

READ THIS TO FIND OUT ABOUT: Achieving high-performance feedback with optocoupler-based differential-resistance. Designing and modelling negative differential behaviour using optocouplers.

Negative Differential Resistance (NDR) is a property of electrical circuits where current is a decreasing function of voltage. The range of voltages for which this occurs is known as a negative resistance region. Ofer Aluf, MSc (Physics), Optoelectronics Technical Specialist, Future Electronics (Israel), describes how NDR devices can be used to make highly-stable, radio-frequency oscillators.

 

The optocoupler as an NDR element

Analogue optocouplers are normally Positive Differential Resistance (PDR) components. However, they can produce NDR behaviour when connected to a specific circuit design in a specific way. This design offers flexibility, since changes to the optocoupler circuit design control the negative differential parameters.

 

 

NDR-circuit operation

The elements of an NDR circuit are relatively simple. The circuit shown in Figure 1 produces NDR behaviour, with the current increasing as the voltage decreases.

An analogue optocoupler (4N35) uses a basic LED to emit light onto a photo-transistor base. This photo-transistor is at the cut-off region as long as the collector-emitter voltage is below the sustaining voltage (V_S). When the terminal voltage (V_CE) of the photo-transistor reaches V_S, the light output from the LED generated by the collector current, due to the avalanche breakdown of the photo-transistor, hits the base window of the photo-transistor.

At this point, the previously cut-off photo-transistor becomes active, and the terminal voltage of the photo-transistor reduces in proportion to the LED light’s intensity. The collector current of the photo-transistor causes a corresponding increase in the light intensity from the LED. The photo-transistor rapidly reaches saturation point due to the regenerative switching action of the optical positive feedback loop from the LED to the photo-transistor.

 

Modelling NDR behaviour

The LED light which strikes the photo-transistor base window can be represented as a dependent current source, depending on the LED’s forward current, with a proportional k constant. The dependent current source is the photo-transistor’s base current:

IB = ILED * k.

The basic Ebers–Moll transistor equations give the following for VCE:

 

For analysis, the optical coupling between the LED (D1) and the phototransistor (Q1) of Figure 2 can be represented as a transistor base current dependent on the LED (D1) current, where:

IB = k * ID1, ID1 = IC1

and:

IB = IC * k

assuming that .

S1 is a dependent current source (I_B = k * I_D1). This circuit assumes that k>1, in order to maintain the saturation process after break-over takes place.

 

 

As long as the photo-transistor is in the cut-off region, the currents IC, IE, and IB will be very low. When the photo-transistor reaches the break-over voltage, the photo-transistor enters the saturation region and V_CE decreases while I_C increases. This is negative differential resistance behaviour.

A positive-feedback loop then begins, in which the transistor’s collector current increases until the photo-transistor reaches saturation state. Finally an expression for voltage against current can be derived for the NDR circuit. In this case (where I_C = I) this expression is:

Here it is assumed that:

The value changes as the process comes closer to the photo-transistor saturation region: dV(I)/dI = f(I, etc)

The dV(I) /dI equation can be shown as a parametric function with some constants. For the region that is after the break-over voltage but near enough to the cut-off region, NDR behaviour can be described thus:

For the region that is near and also in the photo-transistor’s saturation state, NDR behaviour can be described thus:

For the cut-off region before the break-over k=0 generating the expression:

 

Controlling NDR characteristics through optocoupler parameters

Because each optocoupler has its own unique parameters () replacing one optocoupler with another offers the ability to change NDR characteristics.

Given that , the derived NDR equation is:

Therefore the NDR sensitivity for each parameter is:

Assuming that k is constant, and is actually a non-linear function of the NDR current (I), then k=k(I).

 

How to produce oscillations and regenerative amplification using an NDR circuit

The usual procedure for the production of oscillations in LC networks is to overcome circuit losses by designing-in positive feedback or regeneration. An optocoupler-based NDR device offers the oscillator best performance in terms of the cancellation of resistive losses (see Figure 3).

 

 

The total energy (U) present at any instant in the oscillating LC circuit is given by:

System analysis based on the assumption that the circuit resistance is zero, shows that there is no energy transfer to heat and that U remains constant with time:

Where U_total is a constant and dU_total / d_t = 0.

The condition for V_optoNDR = f(I_optoNDR) must fulfil the energy condition:

Therefore:

 

FM radio signal generation

The generator that produces the carrier of an FM waveform is, in many instances, a tuned circuit oscillator. Parasitic resistance is a common phenomenon in such oscillator circuits, but can be eliminated by a conventional NDR element.

 

 

By enabling the smoother operation of an FM generator, an opto NDR gives better performance than conventional NDR elements such as tunnel diodes or Gunn diodes. Such an FM oscillator circuit is shown in figure 4, where L1 is the inductance and C1 the capacitance. This LC combination is in parallel with the opto NDR (the compensation element) and with the parasitic resistance (R1).

In this case:

Therefore an equation for the FM-modulated frequency can be derived:

The capacitance value here, consists of a fixed capacitor (C1) which is shunted by a voltage-variable capacitor (D1). A voltage-variable capacitor, commonly called a Varicap, has a capacitance value that is dependent on the DC-biasing voltage maintained across its electrodes. The FM-modulation signal therefore varies the voltage (Cv) across D1. As a consequence, the capacitance of D1 changes and causes a corresponding change in the oscillator frequency.

 

Conclusion

Analogue optocouplers are very basic components used in many applications. They offer good isolation and the ability to vary the coupling parameters by selecting optocouplers with different specifications. When used to implement an NDR circuit in an application such as a high-frequency oscillator, an optocoupler offers good control of parameters, and an optical mechanism for creating the NDR region. This results in better performance than other commonly used NDR components, such as tunnel diodes and Gunn diodes.