Chapter 10 Analog Systems Microelectronic Circuit Design Richard C. Jaeger Travis N. Blalock Microelectronic Circuit Design, 3E McGraw-Hill

High-pass Amplifier: Description True high-pass characteristic impossible to obtain as it requires infinite bandwidth. Combines a single pole with a zero at origin. Simplest high-pass amplifier is described by wH = lower cutoff frequency or lower half-power point of amplifier. Microelectronic Circuit Design, 3E McGraw-Hill

High-pass Amplifier: Magnitude and Phase Response High-pass filter symbol Bandwidth (frequency range with constant amplification ) is infinite Phase response is given by Microelectronic Circuit Design, 3E McGraw-Hill

Microelectronic Circuit Design, 3E RC High-pass Filter Problem: Find voltage transfer function Approach: Impedance of the where capacitor is 1/sC, use voltage division Microelectronic Circuit Design, 3E McGraw-Hill

Band-pass Amplifier: Description Band-pass characteristic obtained by combining high-pass and low-pass characteristics. Transfer function of a band-pass amplifier is given by ac-coupled amplifier has a band-pass characteristic: Capacitors added to circuit cause low frequency roll-off Inherent frequency limitations of solid-state devices cause high-frequency roll-off. Microelectronic Circuit Design, 3E McGraw-Hill

Band-pass Amplifier: Magnitude and Phase Response The frequency response shows a wide band of operation. Mid-band range of frequencies given by Transfer characteristic is Microelectronic Circuit Design, 3E McGraw-Hill

Band-pass Amplifier: Magnitude and Phase Response (cont.) At both wH and wL, assuming wL<<wH, Bandwidth = wH - wL. The phase response is given by Microelectronic Circuit Design, 3E McGraw-Hill

Narrow-band or High-Q Band-pass Amplifiers Gain maximum at center frequency wo and decreases rapidly by 3 dB at wH and wL. Bandwidth defined as wH - wL, is a small fraction of wo with width determined by: For high Q, poles will be complex and Phase response is given by: Band-pass filter symbol Microelectronic Circuit Design, 3E McGraw-Hill

Band-Rejection Amplifier or Notch Filter Gain maximum at frequencies far from wo and exhibits a sharp null at wo. To achieve sharp null, transfer function has a pair of zeros on jw axis at notch frequency wo , and poles are complex. Phase response is given by: Band-reject filter symbol Microelectronic Circuit Design, 3E McGraw-Hill

Microelectronic Circuit Design, 3E All-pass Function Uniform magnitude response at all frequencies. Can be used to tailor phase characteristics of a signal Transfer function is given by: For positive Ao, Microelectronic Circuit Design, 3E McGraw-Hill

Complex Transfer Functions Amplifier has 2 frequency ranges with constant gain. The mid-band region is always defined as region of highest gain and cutoff frequencies are defined in terms of midband gain. Since wH  w4 and wL  w3, Microelectronic Circuit Design, 3E McGraw-Hill

Microelectronic Circuit Design, 3E Bandwidth Shrinkage If critical frequencies aren’t widely spaced, the poles and zeros interact and cutoff frequency determination becomes complicated. Example : for which Av(0) = Ao Upper cutoff frequency is defined by Solving for wH yields wH = 0.644w1. The cutoff frequency of two-pole function is only 64% that of a single-pole function. This is known as bandwidth shrinkage. Microelectronic Circuit Design, 3E McGraw-Hill