Single Stage Amplifier Frequency Response and Phase Response Curves:

The voltage gain of a single-stage transistor amplifier commences to fall off at some high frequency. This fall-off may be due to the construction of the individual transistor or to stray capacitance in the circuit. Gain-frequency response of single stage amplifier is depicted in Fig. 35.1, the frequency being plotted on a logarithmic base. The voltage gain falls off at a rate of 6 dB per octave i.e. there is a fall off of 6 dB for each doubling frequency, and it can also be stated as 20 dB for each tenfold increase in frequency (-20 dB per decade). The pole frequency fp is the frequency at which the gain is down by 3 dB from its midband value.

Frequency and Phase Response Curves of a Single Stage Amplifier

Figure 35.1 also depicts a graph of phase shift versus frequency for a single-stage transistor circuit. The phase shift increases from zero until it is -45° at the pole frequency fp and continues to increase with increase in frequency to a maximum of -90°, as shown in Fig. 35.1.

Op-amps generally consist of three stages, namely, a differential input stage, an intermediate amplification stage, and low impedance output stage. Each of these stages has its own gain-frequency and phase-frequency response. Usually the pole frequency of second stage is higher than that of stage 1, and the pole frequency of third stage is higher still.

Frequency and Phase Response Curves of a Single Stage Amplifier

A straight-line approximation of gain-frequency response curve for a typical op-amp is given in Fig. 35.2. From the curve shown in Fig. 35.2 it is noted that the overall voltage gain initially falls off at -6 dB per octave or -20 dB/decade from fp1, when only the gain of first stage is decreasing. At pole frequency fp2, second stage gain is now falling off at -6 dB per octave, thus the total rate of fall off is -12 dB/octave or -40 dB per decade. Finally, when the operating frequency becomes equal to fp3 the gain of third stage commences to fall off, and the overall rate of decline of voltage gain is -18 dB/octave or -60 dB/decade.

The phase-shifts of individual stage also add together, as illustrated on the total phase-shift versus frequency curve in Fig. 35.2. At pole frequency fp1, only first stage is effective, and the total open-loop phase shift is -45°. At pole frequency fp2 second stage adds another -45°, but at this point first stage phase shift is at its maximum of -90°. Thus the total phase shift is (-45° – 90°) = -135°. When the frequency becomes fp3, first stage and second stage are each contributing -90° of phase shift, and the third stage adds a further -45°. Consequently, the total phase shift at pole frequency fp3 is -225°(-90° – 90° – 45°). This open-loop phase shift is in addition to the -180° phase shift that normally occurs from the op-amp inverting input terminal to the output.

As already discussed, oscillations occur when loop gain Aβ ≥ 1 and loop phase shift Φ is -360°. In fact it is not necessary that phase shift may be -360° for oscillation to occur. A phase shift of -330° at Aβ ≥ 1 makes the circuit unstable. The total loop phase shift must not exceed -315° when Aβ = 1, so as to avoid oscillations. The difference between the actual phase shift Φ at Aβ = 1 and 360° is known as phase margin. For stability, the phase margin should not be less than 45°.

As the Single Stage Amplifier Frequency Response is shown in Fig. 35.2, the maximum gain is 100 dB, which is equivalent to a voltage gain of 105.

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