Decibel’s AND LOGARITHMIC PLOTS Decibels Frequency-response data arc often presented in decibel form. Recall that decibels (dB) are the units used to compare two power levels in accordance with the The two power levels, PI and P2, are moisten the input and output power of a system, respectively, in which case equation 10-3 defines the power gain of the system in decibels. If P2 > PI, t icn equation 10-3 gives a positive number, and if P2 < PI,
the result is negative, sign-frying a reduction in power. If P2 = PI, tilt: result is 0 dB. since logo(1) = O. Let RI be the resistance across which the power PI is developed and R2 be the resistance across which P2 is developed. Then, since P = v2/ R, we have. from equation 10-1 where V2 is the fins voltage across R2 and VI is the rms voltage across RI• If the resistance values are the same ‘at the two points where the power comparison is made (R\ = R1. = R), then Equation 10-5 gives p we gain (or loss) in terms of the voltage levels at two points in a circuit, but it must be remembered that the equatorial for power comparison only if the resistances at the two points arc equal. The same emo union is used to compare voltage levels regardless of the resistance values at the two points. In other words, it is common practice to compute voltage gain as If the resistances RI and R2 are equal, then the power gain in dB equals the voltage gain in dB.The amplifier shown in Figure 10-4 has input resistance 1500n and drives a 100-n load. if the input current is 0.632 mA rills and the load voltage is 30 V rems, find
1. the power gain in dB; and
2. the voltage gain in dB.
It is helpful to remember that a two-to-one change in voltage corresponds to approximately 6 dB, and a ten-to-one change corresponds to 20 dB. The sign (±) depends on whether the change represents an increase or a decrease in voltage. Suppose, for example, that VI = R V rms. If this voltage is doubled (V2 = 16 V
rms), then Every time a voltage is doubled, an additional 6 dB is added to the voltage gain, and every time it is increased by a factor of 10. an additional 20 dB is added to the voltage gain. For example, a gain of 100 = 10 X 10 corresponds to 40 dB and a gain of 4 corresponds to 2 X 2 = 12 ‘dB. As another example. a gain of 4(10 = 2 x 2 x 10 x 10 corresponds to (6 + 6 + 20 + 20) dB = 52 dB. Similarly, a reduction in voltage by a factor of 0.05 = (1/2)(1110) corresponds to -6 – 20 = -26 dB. Common logarithms (base 10) can be computed on most scientific-type calculators, and the reader should become familiar with the calculator’s use for that purpose and for computing inverse logarithms. For reference and comparison purposes, Table 10-1 shows the decibel values corresponding to some frequently encountered ratios between 0.001 and 1000 The input voltage to an amplifier is 4 rms. At point 1 in the amplifier, the voltage gain with respect to the input is -4.2 dB and at point 2 the voltage gain with respect to point 1 is 18.5 dB. Find
I. the voltage at point I;
2. the voltage at point 2; and
3. the voltage gain in dB at point 2, with respect to the input. Solutio”. Let v the input voltage (4 X 1O-J Y rms), v, = the rms voltage at point 1, and V2 = the rms voltage at point 2.
(On most scientific calculators, the inverse log of -0.21 can be computed directly by entering a sequence such as -0.21, inverse, log; it can also be found on a calculator having the yX function by computing It must be remembered that decibels arc derived 1rom a ratio and therefore represent a comparison of one voltage or power level to another.correct to speak of voltage or power gain in terms of decibels, but it IS meaningless to speak of output level in dB. unless the reference level is specified. Popular publications and the broadcast media frequently abuse the term decibel because no reference level is reported. Do not be confused by this practice. It is common practice in some technical fields to use one standard reference level for all decibel computations. For example, the power level 1 mW is used extensively as a reference. When the reference is 1 mW, the decibel unit is write en dim: