The high-frequency response of an amplifier is characterized by the transfer function [latex]F_{H}(s) = \frac{1 − s/10^{5}}{(1 + s/10^{4})(1 + s/4 × 10^{4})}[/latex] Determine the 3-dB frequency approximately and exactly.

Noting that the lowest-frequency pole at [latex] 10^{4}[/latex] rad/s is two octaves lower than the second pole and a decade lower than the zero, we find that a dominant-pole situation almost exists and ω H [latex]\simeq 10^{4}[/latex] rad/s. A better estimate of ω H can be obtained using Eq. (10.77), as follows: [latex]ω_{H} \simeq 1 / \sqrt{\left(\frac{1}{ω_{P1}^{2}} + \frac{1}{ω_{P2}^{2}} + ...\right) - 2\left(\frac{1}{ω_{Z1}^{2}} + \frac{1}{ω_{Z2}^{2}} + ...\right) } [/latex] (10.77) [latex]ω_{H} = 1 / \sqrt{\frac{1}{10^{8}} + \frac{1}{16 × 10^{8}} - \frac{2}{10^{10}}}[/latex] = 9800 rad/s The exact value of ω H can be determined from the given transfer function as 9537 rad/s. Finally, we show in Fig. 10.23 a Bode plot and an exact plot for the given transfer function. Note that this is a plot of the high-frequency response of the amplifier normalized relative to its midband gain. That is, if the midband gain is, say, 100 dB, then the entire plot should be shifted upward by 100 dB.

Question 10.7: The high-frequency response of an amplifier is characterized...

Microelectronic Circuits

The high-frequency response of an amplifier is characterized by the transfer function

$F_{H}(s) = \frac{1 − s/10^{5}}{(1 + s/10^{4})(1 + s/4 × 10^{4})}$

Determine the 3-dB frequency approximately and exactly.

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Noting that the lowest-frequency pole at $10^{4}$ rad/s is two octaves lower than the second pole and a decade lower than the zero, we find that a dominant-pole situation almost exists and ω_H $\simeq 10^{4}$ rad/s. A better estimate of ω_H can be obtained using Eq. (10.77), as follows:

$ω_{H} \simeq 1 / \sqrt{\left(\frac{1}{ω_{P1}^{2}} + \frac{1}{ω_{P2}^{2}} + …\right) – 2\left(\frac{1}{ω_{Z1}^{2}} + \frac{1}{ω_{Z2}^{2}} + …\right) }$ (10.77)

$ω_{H} = 1 / \sqrt{\frac{1}{10^{8}} + \frac{1}{16 × 10^{8}} – \frac{2}{10^{10}}}$

= 9800 rad/s

The exact value of ω_H can be determined from the given transfer function as 9537 rad/s. Finally, we show in Fig. 10.23 a Bode plot and an exact plot for the given transfer function. Note that this is a plot of the high-frequency response of the amplifier normalized relative to its midband gain. That is, if the midband gain is, say, 100 dB, then the entire plot should be shifted upward by 100 dB.