11.5. Frequency Response of the Operational Amplifier and Resistor Feedback Amplifier

The MOSFET has a number of capacitances, including those associated with the gate structure and source and drain pn junctions as well as other parasitic capacitors of the transistor and the circuit. Therefore, the open-loop opamp will tend to be unstable due to the poles and zeros associated with the capacitors. Opamps are usually stabilized with the addition of a capacitor. The added pole is well below the lowest naturally occurring pole. This pole will dominate the frequency response of the opamp. In a lab project, the pole frequency will be measured.

We will obtain the frequency response of the feedback amplifier based on the single-pole response. The form of the response of the open-loop opamp is

Equation 11.17

The response function has value a_vo at low frequencies and has magnitude at f = f_{3dB opamp}, where f_{3dB opamp} is the characteristic frequency of the opamp. This is indirectly, f_{3dB opamp} = GBP/a_vo, where GBP is the gain – bandwidth product of the opamp as given in the datasheet. Datasheet value a_vo is also given (A_vd, large-signal voltage gain).

The noninverting feedback amplifier has a gain as given by (11.3). That expression is used here along with (11.17) in place of a_vo. The frequency response of the feedback amplifier is thus

Equation 11.18

which is

Equation 11.19

This can be simplified to

Equation 11.20

where A_vo is the amplifier gain at low frequencies and where

Equation 11.21

Frequency parameter f_BW is the bandwidth of the amplifier for a specific A_vNI · Parameter f_BW, by definition of bandwidth, is also f_3dB of the amplifier. Adding feedback by reducing R_f always increases bandwidth at the expense of gain. Note that for R_f very small, f_BW can be relatively high and the frequency response is complicated by the fact that other poles of the opamp come into play.

Given in Table 11.1 is a segment from the manufacturer’s datasheet for the opamp (TS271C) used in our project. As mentioned above, the parameter for large-signal voltage gain is designated as A_vd and is identical to a_vo. The GBP indicated is 700 kHz. Thus for a low-frequency amplifier gain of, for example, A_v = 5000, the bandwidth is f_BW = 700 kHz/5K = 140 Hz, which can be readily measured using LabVIEW and the DAQ in the computer.

TABLE 11.1
Symbol	Parameter	TS271C/AC/BC			Unit
		Min.	Typ.	Max
Avd	Large Signal Voltage Gain VO = 1 V to 6 V, RL = 100 kΩ, Vic = 5 V Tmin. < Tamb < Tmax.	30 20	50		V/mV
GBP	Gain Bandwidth Product (Av = 40dB, RL = 100 KΩ, CL = 100pF, fin = 100 KHz)		0.7		MHz

Note that for the limiting case of R_f → ∞, the bandwidth of the open-loop amplifier is only f_3dB = 700 kHz/50K = 14 Hz, where the typical (Typ.) number, A_vd = 50 k has been used.