Return to this week's Bulletin

30 November 2001

Negative Resistance Amplifiers

by Kevin Kilty

Most of us recognize thermistors as temperature sensitive resistors. They act as temperature sensors, and they also provide temperature compensation in some types of circuitry. Since these devices are resistive by nature a person might be inclined to think of them as dissipative only. However, thermistors are capable of much more complex behavior.

The diagram below is data that I acquired using a FenWal precision thermistor. It is called a characteristic curve of the thermistor. The graph shows the relationship of current passing through the device to the voltage drop across it. From zero to a milliampere of current the voltage rises with increasing current as a person expects from a resistive device. However, beyond a milliampere of current the voltage drop across this thermistor begins to decline with increasing current.

Figure 1. Curve of characteristic behavior for a FenWal Precision thermistor. Beyond 1mA current the thermistor displays negative resistance behavior.

If I define differential resistance as dV/di, then this thermistor is now in a state of negative resistance. Before I go on to discuss this behavior, I should explain why it occurs. As a thermistor carries substantial current it will become warm. Because the resistance of a thermistor declines rapidly with increasing temperature, it is possible to reach a state where increased current warms a thermistor sufficiently to lower its resistance irrespective of the ambient temperature. This implies, of course, that the characteristic curve of a thermistor is not a function of the current through the device alone, but also depends on how the device interacts thermally with its surroundings.

Now what is the consequence of such behavior? Figure 2 shows an amplifier circuit based on the thermistor. The inductor, battery, bias resistor and thermistor are in a series circuit that comprises the amplifier. If we think of the DC behavior of this circuit, then the inductor has no effect (it behaves as a short circuit for DC), and the bias resistor simply limits current from the battery to place the thermistor on the negative resistance portion of its characteristic at Q. This is what is meant by the term bias current.

Figure 2. Circuit of an "insertion" amplifier based on a thermistor.

Figure 3 illustrates how the circuit works. If I imagine taking the thermistor out and leaving the circuit open, then the open circuit would have a voltage of V_t=V_b. Engineers call this the Thevenin voltage. Now imagine replacing the thermistor with a short circuit. Now a current of I_n=V_b/R_b will flow in the circuit. Engineers call this the Norton current. Figure 3 shows a line drawn from the Thevenin voltage to the Norton current. This is known as the load line, and it is very useful for describing the circuit operation. If we superimpose the load line on the device characteristic, as I have done, the point of intersection is where the circuit will operate. In figure 3 the operating point is on the negative resistance portion of the characteristic.

Figure 3. Load line analysis of the insertion amplifier. The point Q is the point of quiessent operation. Resistor R_b and supply voltage, V_b are chosen to make Q the point of intersection of the load line and the characteristic when there is no signal. Note in particular that the load line must cross the characteristic from above or the amplifier is not stable, it may oscillate or latch-up depending on how the characteristic curve behaves further to the right.

Now imagine how this circuit will behave if we apply a varying signal to its input capacitor. As voltage at 'A' varies, the capacitor will draw or supply current. The inductor will prevent this current from being drawn from the battery (an inductor acts as a resistor for AC) and current through the thermistor will, therefore, have to change. In effect, the load line varies right and left almost parallel to itself. This will move the point of operation up and down along the negative resistance slope. The result is that an input signal causing a small variation in voltage V_t, will change the output voltage at 'B' by a larger amount. A magnified view of the load line and characteristic are shown in Figure 4. A small change in input current, DL, will lead to a somewhat larger change in operating point, DQ. The signal is amplified by a dissipative device!

Figure 4. A closer load line analysis. A small change in input current (the signal) moves the load line approximately parallel to itself, leading to a large change in operating point. Of course, the signal has to be slow enough for temperature changes to actually move the circuit along the characteristic.

 

Thermistors depend on heat flow to form the negative resistance characteristic, and because heat flow is a slow process generally, an amplifier built on this circuit cannot amplify high frequency signals.

In order to extend this idea, I suggest the following observation. All of us have observed an expensive nightlight oscillate (flutter) when it operates during the day or in dim light. This observation tells us that the night light has a negative resistance characteristic, but unlike the circuit I have described above, the load line and charcteristic intersect at an unstable quiessent point. Can someone describe how to build a device from a CdS photocell and passive components which displays negative resistance and which could serve in an insertion amplifier?

Devices like this may not be important technologically, but they could make for a fun science fair project.