Figure 5.2b showed a system based on 5.2a, but with the single resistor, *R*, replaced by a *load* resistance, , and a Gunn diode which has a negative dynamic resistance, . Figure 5.4 shows how the total dynamic resistance of this combination depends on the voltage across the diode.

A D.C. voltage is applied to the diode via an extra inductance (whose value is very large). As a result we arrange that average voltage on the Gunn diode is as illustrated in figure 5.4. The diode is said to be *biassed* into the negative resistance region. Any small fluctuations at the oscillation frequency will tend to grow because, for voltages the total circuit dynamic resistance, . The oscillation causes the diode voltage to swing back and forth about . As this swing grows it eventually spreads into the regions where .

Whilst in the region the energy of any oscillation tends to be reduced by resistive dissipation. Whilst in the region the oscillation energy tends to be increased. As a result the size of the oscillation tends to stabilise at a size where the amount of energy per cycle ‘generated’ while in the region equals that dissipated per cycle while in the region.

We can simplify things by representing this behaviour in terms of an “averaged” device negative resistance value, , whose value depends upon, *i*, the rms size of the oscillation current. In effect, , is the value of averaged over one oscillation cycle. When the oscillation is small . Allowing the device voltage to swing over a larger range makes it spend more time at ‘less negative’ resistance values. Hence tends to vary with oscillation current as illustrated in figure 5.5. The steady oscillation amplitude will be determined by the size of the current/voltage swing which causes the average value of As with feedback oscillators there are therefore two conditions which must be satisfied for oscillation to take place. Firstly, the amplitude of the oscillation will be such that.

secondly, the oscillation frequency will be

The oscillatory power ‘generated’ by the negative resistance oscillator comes from the D.C. bias power, , which we have to provide to maintain an average diode voltage in the negative resistance region. As the principle of conservation of energy requires that it follows that the negative resistance region can __never__ include zero volts. Furthermore, to ensure that we are always having to put bias power into the system it must also be true that . This means that the mean current and voltage always share the same sign — i.e. the __static__ resistance must always be positive.

In practice the amount of power we can get from the oscillator will depend upon how large a range of voltages and currents the negative resistance region covers. We can therefore expect that

where and are the current values at the peak and valley voltages.

Gunn oscillators are widely used in the microwave to Terahertz region. A typical oscillator is shown in figure 5.6. This uses a metallic *coaxial cavity* (in effect, a short length of co-axial cable) to provide the resonant effect which has been modelled earlier as an *LC* circuit. Although it looks very different, the oscillator shares with a laser the use of a cavity. The size of this cavity determines the time/phase delay which sets the resonant frequency. In this case, each diode induced fluctuation travels up the cavity and reflected from the far end, returning to the diode after a time

where *l* is the cavity length & *c* is the speed of light along the cavity.The oscillator may therefore oscillate at any frequency such that

where *n* is the “number of half-waves” we can fit into the cavity at a given frequency. In practice, the diode will take a time, , to react to any change in the voltage across it. This time is determined by the physical processes which cause the Gunn effect. Since the diode takes to respond to a voltage increase and to a decrease we can't expect it to oscillate at a frequency greater than about . This means that the oscillator can only operate at frequencies such that

Looking at 5.13 we can see that the maximum possible oscillation frequency is determined by the diode's *response time*, . When we want a high frequency oscillator it makes sense to use the shortest possible cavity length so that

This ensures that the only possible oscillation *mode* is the one where i.e. the system won't oscillate at a lower frequency because the cavity is too short to permit it. It can't oscillate at a higher frequency because the diode is ‘too slow’, hence we ensure a single-valued oscillation frequency.

Real Gunn devices have a response time which varies with the applied voltage, hence we can *electronically tune* the oscillation frequency by slightly adjusting the bias voltage, changing , and hence altering . Although too complicated to consider in detail here it is also worth noting the fact that, since the diode's I/V relationship is curved the oscillation currents and voltages in the circuit won't actually be sinusoidal. The arguments presented above tell us the ‘fundamental’ oscillation frequency. However, the system will also generate power at *harmonics* of this frequency. This property of harmonic production is useful. Conventional GaAs Gunn devices can't oscillate above about 65GHz, yet they are routinely used as 90-140GHz sources. These mm-wave oscillators extract the first harmonic from an oscillator which is actually oscillating at half the observed output frequency.

In fact, the negative resistance oscillator is just a special form of a feedback oscillator. A negative resistance provides *gain* (it increases the power of a fluctuation). The cavity acts as a feedback arrangement, taking the diode's output and returning it again after a set time/phase delay.

Summary.

You should now know how a combination of a *Negative Resistance* and a *Cavity* or *Resonant Circuit* can work as a coherent oscillator. That the amount of power such an oscillator produces is limited by the bias power and the size of the negative resistance region. That a ‘true’ negative resistance is impossible since it would be able to generate oscillatory power out of nothing, hence violating the principle of energy conservation. Hence a more precise term for this form of an oscillator would specify negative *Differential* or *Dynamic Resistance/Conductance*. It should also be clear that the oscillator has something in common with a laser since it uses a cavity to control its operation. It also acts in some ways like a specialised feedback oscillator since it combines gain with a feedback arrangement.

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