BJT and JFETFrequency Response

LOW-FREQUENCY ANALYSIS—BODE PLOT

R-C Combination that will define a low cut-off frequency

R-C circuit at very high frequency

R-C circuit at f = 0 Hz

Between the two extremes, the ratio Av = Vo/Vi will vary as shown in the figure.As the frequency increases, the capacitive reactance decreases and more of the inputvoltage appears across the output terminals.

Low frequency response for the R-C circuit

The output and input voltages are related by the voltage-divider rule in the fol-lowing manner:

with the magnitude of VO determined by

For the special case where X C = R,

and,

the level of which is indicated on the previous figure. In other words, at the frequency of which XC = R, the output will be 70.7% of the input for the network.The frequency at which this occurs is determined from

and,

and using the frequency defined above,

If the gain equation is written as

In the magnitude and phase form,

For the magnitude when f = f1 ,

In the logarithmic form, the gain in dB is

For frequencies where f << f 1 or (f 1 / f) 2 >> 1, the equation above can be approximated by

and finally,

Ignoring the condition f << f 1 for a moment, a plot of the previous equation on a frequency log scale will yield a result of a very useful nature for future decibel plots.

A plot of these points is indicated in the next figure from 0.1 f 1 to f 1 . Note that this results in a straight line when plotted against a log scale. In the same figure, a straight line is also drawn for the condition of 0 dB for f >> f 1 . As stated earlier, the straight line segments (asymptotes) are only accurate for 0 dB when f >> f 1 and the sloped line when f 1 >> f. We know, however, that when f = f 1 , there is a 3-dB drop from the mid-band level. Employing this information in association with the straight-line segments permits a fairly accurate plot of the frequency response as indicated in the same figure. The piecewise linear plot of the asymptotes and associated breakpoints is calleda Bode plot of the magnitude versus frequency.

Example: For the network:

(a) Determine the break frequency.(b) Sketch the asymptotes and locate the -3dB point.(c) Sketch the frequency response curve.

Solution:

For frequencies f << f 1 ,

For instance, if f 1 = 100f,

For f = f 1 ,

For f >> f 1 ,

For instance, if f = 100 f 1 ,

A plot of = tan -1 (f 1 /f ) is provided in the next figure. If we add the additional 180° phase shift introduced by an amplifier, the phase will be obtained. The magnitude and phase response for an R-C combination have now been established. In the next section, each capacitor of importance in thelow-frequency region will be redrawn in an R-C format and the cutoff frequency for each determined to establish the low-frequency response for the BJT amplifier.

- Phase response for the R-C circuit