The expression “nonlinear” sounds like mathematics but, relax, this article is not about math, it’s about practical electronics… OK, allow me only a little bit of Ohm’s law to demonstrate a few points!
In a world dominated by digital electronics, one easily forgets about the effect some components characteristics have when used in analogue circuits. Indeed, the realm of electronics is made of a wide variety of components. Some are linear and some are not. Circuit’s designers avoid nonlinear components in some designs because they have the potential to distort electrical signals. In some other circuits, designers will use their nonlinearity for their purpose.
A linear component is one that has a linear relationship between current and voltage. A nonlinear component, on the other hand, has a nonlinear relationship between voltage and current (except for the potentiometers discussed later!). The best way to understand this is to compare a resistor with a diode, as shown in figure 1. To all of us, a diode is a simple component that conducts electricity in one direction and not in the other. In this article we will have a closer look at one of the diode’s characteristic curve because it helps to understand non-linearity.
In the circuit above, we gradually increase the voltage across the component and measure the resulting current. Then we plot a graph of the current versus the voltage as shown in the figure. No math, I promised, but let’s play with the Ohm’s law…
The resistor’s plot will show a straight line (hence the word linear = straight). At any point of the graph we can calculate the resistance by a simple application of the Ohm’s law. At 0.2V we have around 125mA, at 0.4V we have around 250mA etc… Double the voltage and the current will double as well. The relation is linear, or proportional. At any point of the graph the result of Voltage divided by Current will be the same i.e. 1.6 Ohm in our example.
The diode is a different story. For this diode, we can increase the voltage from zero until around 0.7V before measuring any noticeable current. In this area of its characteristic the diode behaves like an insulator (almost!). Beyond 0.7V the current starts to increase, first slowly, then faster as the voltage increases. Beyond 0.9V the characteristic starts to look like the one from the resistor. It is interesting to note that this particular diode (1N4148) is nearly linear for a large part of its characteristic curve but overall it is a nonlinear component. This should not be taken as a general rule because other types of diodes might present a curvier characteristic all the way.
Unlike with the resistor, we cannot calculate the resistance value by dividing voltage by current at any point of the curve and expect to find the same value. Let’s try with P1 (1V and 150mA = 6.6 Ohm) and P2 (1.4V and 450mA = 3.11 Ohm). Sure it’s not linear… Some literature says it doesn’t obey the Ohm’s law. Indeed it does, but only for a specific point of the curve. This is called the static resistance of a diode and it is different for each point of the curve (even the linear part) as we just demonstrated.
Only for the fun of it, let’s see how the diode reacts to voltage changes, within its linear zone. As it is almost parallel with the resistor we would expect a similar value, maybe slightly lower because it is a bit more towards vertical. The way to do is to take two points (P1 and P2) and divide the difference of voltage by the difference of current as follows:
P1 = 1V and 150mA
P2 = 1.4V and 450mA
R = (1.4V – 1V) / (450mA – 150mA) = 0.4V / 300mA = 1.33 Ohm
This is called the dynamic resistance of the diode and is more like what we expected by looking at the graph. This value will be the same for any two points within the linear zone.
The Point where the Diode starts conducting is called the diode threshold or “turn-on voltage”. It is around 0.6 to 0.7V for silicon diodes. This value is different for other diode types. Schottky diodes have a threshold of 0.2 to 0.3V, Germanium diodes 0.25 to 0.3V and LEDs 2 to 2.5V. High Voltage Diodes can have a threshold from 4V up to 35V, depending on the maximum reverse voltage.
Thanks to our good old analogue multimeter we can test diodes having a threshold up to 12V using the X10K Ohm scale. For more information on how to measure you can refer to Jestine Yong’s excellent book “Testing Electronic Components”. Figure 2 shows the measurement of a High Voltage Diode. The digital voltmeter indicates the threshold value which is close to 6V.
Just like the diode, other semiconductors such as transistors are nonlinear devices. Iron core transformers and inductors are linear up to their saturation level. Above saturation they become nonlinear. Many components have a part of their characteristic curve that is linear, or almost. The art of electronics consists of using the linear region of the curve when a linear response is requested.
As an example, a transistor amplifier (correctly biased) will be linear at low signal levels but will become nonlinear at high signal levels. You can hear it when you listen to the distortion an audio amplifier produces when the volume is turned to the maximum. The figure 3 illustrates the distortion caused when the signal level goes beyond the linear zone of an amplifier.
All this seems very troublesome but, in reality, it is challenging and interesting. Would a totally linear world be a better place to live? Not really, the natural world shows much nonlinear behaviour and most for good reasons. One of the most interesting, because it affects electronic circuits, is the way the human hear perceives the sound. The human hear is unbelievably sensitive and, at the same time, can hear noises up to 1 trillion times more powerful than the smallest audible sound. Psychologists say that our sense of hearing is roughly logarithmic which explains why we can hear within such a wide range of intensity. To say it simply, if you hear one man playing the piano, you will need 10 pianists to have the perception that the sound intensity is double and 100 pianists for triple etc… The human perception of the intensity of sound is more nearly proportional to the logarithm of intensity than to the intensity itself. It I is why we use decibels (dB) to express sound levels.
On the decibel scale, the smallest audible sound (near total silence) is 0dB. A sound 10 times more powerful is 10dB. A sound 100 times more powerful than near total silence is 20dB. A sound 1,000 times more powerful than near total silence is 30dB. Please note the progression 0, 10, 20, 30 for 1, 10, 100, and 1000. Similar to our pianists…
Back to our audio amplifier, we want a linear amplification (no distortion) but we would like the volume control to appear linear, despite our hearing perception which is not linear. This is why logarithmic potentiometers were designed. A logarithmic potentiometer has a resistive element that is made from a material whose resistivity varies from one end to the other. This results in a device where output voltage is a logarithmic function of the mechanical angle of the potentiometer.
For a linear potentiometer, when the cursor is turned half way, the resistance between the cursor and either ends is the same. For example a 100K potentiometer with the knob turned half way will measure 50K for each half. On another hand, a logarithmic potentiometer with the knob turned half way will have very different measurement for each half. For example a 100K logarithmic potentiometer with the button half way will measure approximately 18K from one end to the cursor and 82K from the cursor to the other end. It is important to note that the non-linearity of this component has nothing to do with a nonlinear relationship between voltage and current but rather a nonlinear relationship between rotation angle and resistance! Actually it is used to gives a linear perception of a nonlinear behaviour!
Of course, modern audio systems use digital circuitry to control the volume, so remote controls can be used. In such cases the software or digital circuits will simulate the logarithmic functions. However, the good old “log pot” is still out there in some equipment models.
Other types of nonlinear potentiometers are used in industrial instrumentation or scientific instruments with various characteristics. The Figure 4 shows a few examples of nonlinear curves that can be found on those components.
In conclusion, there is much more in a component’s specifications than its maximum ratings. This can be relevant to the electronic circuit repairer or not, depending on the situation. Replacing a diode used as a common rectifier with another diode of same or higher ratings might work just fine. However, replacing a Schottky diode used as a RF detector or demodulator circuit with a silicon diode will not work at all.
In any case, one should try whatever is possible to find the exact same type replacement.
Penang, 23 June 2011