Equal Voltage Method

Author: Leonard Krugman

The equal voltage method is a quick way of determining the input or output resistance of a system when the equipment is limited. This connection is illustrated in Fig. 4-18 (A).

Resistor R is a calibrated decade box or a helipot in series with the effective input resistance of the system under test. Resistor R is adjusted until its voltage drop V is equal to the input voltage V₁. Since the arrangement is a simple series circuit, the input resistance r₁ is then equal to R.

Figure 4-18 (B) illustrates the equal voltage method for measuring a negative resistance. In this case, a calibrated resistor R₁ having a larger absolute value than that of the negative resistance is connected in series with r₁. Again resistor R is adjusted until V = V₁, for which R - R₁ = r₁. For example, suppose a point-contact transistor is operating in its negative resistance region. When a resistor R = 2,000 ohms is placed in series with the input, it brings the circuit into its positive input region (stable operation). When the connection of Fig. 4-18 (B) is set up, R = 1,225 causes V to equal V₁. Then r₁ = R - R ₁ = 1,225 -2,000 = -775 ohms.

Fig. 4-18. Equivalent voltage method of measuring system input or output resistance.

Notice that this latter arrangement requires that R be greater than the absolute value of r₁. If the only calibrated resistors available are low in value, the parallel method illustrated in Fig. 4-18 (C) can be used. The procedure is the same as before except that when V = V₁, R is equal to R₁ and r_i in parallel,

which in terms of the inputresistance becomes:

For the same transistor measured above, if R₁ = 500 ohms, R is adjusted to 1,408 ohms, at which time V = V₁. Then r_i = = 775 ohms.