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# Linear and Non-Linear Circuit Elements

Author: J.B. Hoag

Imagine, if you will, a sealed box containing electrical circuits of some sort or other, and having four binding posts, two for the "input" and two for the " output." Let the output current I be observed for a succession of voltages E applied to the input terminals, and let a plot be made of these two quantities, with I vertically and E horizontally. If the I-E curve which is obtained is a straight line, the electrical devices in the box are to be called linear elements; if a curved line results, the box contains nonlinear elements.

If the "circuit elements" in the box consist merely of a series resistance, the symmetrical straight line of Fig. 23 A will be obtained.

 Fig. 23 A. Symmetrical ohmic element

Let a fluctuating voltage (e-t) be applied to the input terminals. Then the fluctuating output current (i-t), as shown in this figure, will have the same shape as that of the input voltage.

If the circuit elements consist of crystals, such as galena or iron pyrites, or if they consist of copper-oxide rectifiers, the unsymmetrical, non-linear (= non-ohmic) curve of Fig. 23 B will be obtained.

 Fig. 23 B. Non-ohmic unsymmetrical element

A pure sinusoidal voltage at the input will not yield an output current of the same (sinusoidal) wave-form. Instead, the current will be partially rectified, as shown in the figure, and will be distorted or "full of harmonics".

If the box contains a diode, the detector or rectifier property shown in Fig. 23 C will result.

 Fig. 23 C. Half-wave non-ohmic element

These conditions were discussed in some detail in earlier chapters. The rectifying action of a triode operating on the upper knee of its characteristic curve is shown in Fig. 23 D.

 Fig. 23 D. Rectifier action on the upper knee of a triode

Figure 23 E shows the output currents versus input grid voltages of triodes operated from a point in the middle of the straight portion of the characteristic curve. Notice that when too great an input voltage is used, the upper and lower knees of the characteristic curve are in use and the tops and bottoms of the output current are "squared off".

 Fig. 23 E. Distortion in Class A amplifiers. Also, the principle of limiters

This principle is undesirable in some applications, such as amplifiers, where it is called distortion, but it is useful in other applications, such as current-limiting devices and square-wave generators.

When the grid of a triode is made quite positive, it diverts considerable numbers of electrons to itself. Then the plate current falls off, as indicated by the drop in the upper end of the curve in Fig. 23 F.

 Fig. 23 F. Grid current distortion

An extremely large grid voltage fluctuation gives rise to the peculiar dip in the top of the square wave.

 Fig. 23 G. A "characteristic" curve which yields an unusual double-pulse output

Figure 23 G shows the output current versus input voltage for an electrical device called a "thyrite bridge circuit". Note that the output has a double hump, or frequency, for each half-cycle of the applied voltage.

 Fig. 23 H. Class B amplification

Figure 23 H shows the characteristic curve of an ordinary triode whose C-bias is so negative that the operating point is located at the cutoff point, i.e., for Class B amplification. The output current in this case is rectified. Class C amplifiers are operated with the C-bias well to the left of the cutoff point.

Last Update: 2009-11-01