Microelectronic Circuit Design, 3E McGraw-Hill 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  H = lower cutoff frequency or lower half-power point of amplifier.

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

Microelectronic Circuit Design, 3E McGraw-Hill 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    and  L, assuming  L <<  H, Bandwidth =  H -  L. 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   and decreases rapidly by 3 dB at    and  L. Bandwidth defined as  H -  L, is a small fraction of   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   and exhibits a sharp null at  o. To achieve sharp null, transfer function has a pair of zeros on j  axis at notch frequency  o, and poles are complex. Phase response is given by: Band-reject filter symbol

Microelectronic Circuit Design, 3E McGraw-Hill 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  o,

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      and  L   ,

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