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DMT 231/3 Electronic II Lecture V Low Frequency Response of BJT Amplifiers Effect of Coupling Capacitors mid-band frequencies: coupling & bypass capacitors shorts to ac low frequencies: capacitive reactance affect the gain & phase shift of signals must be taken into account FREQUENCY RESPONSE : the change in gain or phase shift over a specified range of input signal frequencies Effect of Coupling Capacitors 1 XC 2fC capacitive reactance varies inversely with frequency Effect of Coupling Capacitors: Example Figure 1 Effect of Coupling Capacitors: Example • At low freq (audio freq: 10 Hz) less voltage gain (then they have at higher freq): Figure 1 More signal voltage is dropped across C1 & C3 (higher reactances : reduce voltage gain) Reactance of C2 becomes significant & the emitter is no longer at ac ground. Nonzero reactance of the bypass capacitor in parallel with RE creates an emitter impedance, (Ze), which reduces the voltage gain. Figure 2 Effect of Internal Transistor Capacitances Internal transistor capacitances reduce amplifier gain & introduce phase shift as the signal frequency increases Cbe: base-emitter junction capacitance Cbc: base-collector junction capacitance Figure 3 AC equivalent circuit for a BJT amplifier showing effects of the internal capacitances Cbe and Cbc. Figure 4 Miller’s Theorem General case of Miller input and output capacitances. C represents Cbc Figure 5 Amplifier ac equivalent circuits showing internal capacitances and effective Miller capacitances. Figure 6 Decibel • Logarithmic measurement of the ratio of one power to another OR one voltage to another Ap(dB) = 10 log Ap Ap = Pout / Pin Av(dB) = 20 log Av Av = Vout / Vin O dB Reference • Reference gain (no matter what its actual value is) used as a reference with which compare other values of gain Midrange gain • Maximum gain occurs for the range of freq between the upper & lower critical freq Normalized • Midrange voltage gain is assigned a value of 1 or 0 dB. Normalized voltage gain versus frequency curve. Figure 7 Critical Frequency • Also known as cutoff frequency OR corner frequency Frequency at which the output drops to one-half of its midrange value. Corresponds to a 3 dB reduction in the power gain: Ap(dB) = 10 log (0.5) = - 3 dB Power Measurement in dBm • dBm : unit for measuring power levels referenced to 1 mW Low Frequency Amplifier Response A capacitively coupled amplifier Figure 8 The low-frequency ac equivalent circuit of the amplifier consists of three high-pass RC circuits. Figure 9 Input RC circuit formed by the input coupling capacitor and the amplifier’s input resistance. Figure 10 Input RC Circuit The base voltage for the input RC circuit: R in V Vbase R 2 X 2 in in C1 when Vbase Rin R2 R2 in in X C1 Rin R in V in 2 R 2 in V 1 V 0.707V in in 2 in Lower critical frequency Condition where the gain is down 3 dB: overall gain is 3 dB less than at midrange freq a.k.a lower cutoff freq, lower corner freq, or lower break freq. X C1 1 2f cl (input) C1 f cl ( input) Taking into account the input source resistance f cl (input) Rin 1 2Rin C1 1 2 RS Rin C1 Bode Plot Decade: ten times change in frequency Bode Plot: a plot of dB voltage gain versus frequency on semilog graph paper Figure 11 dB voltage gain versus frequency for the input RC circuit Phase angle versus frequency for the input RC circuit. tan Phase angle in an input RC circuit For midrange frequencies At critical frequency X C1 0 X C1 Rin tan 1 Figure 12 X C1 10Rin X C1 R in 0 0 Rin tan 1 At a decade below the critical frequency 1 Rin 45 Rin 10Rin 84.3 Rin tan 1 The input RC circuit causes the base voltage to lead the input voltage below midrange by an amount equal to the circuit phase angle, . Figure 13 Development of the equivalent low-frequency output RC circuit. Output RC Circuit f cl ( output) 1 2 RC RL C3 X C3 tan RC RL Phase Shift in Output RC Circuit 1 Figure 14 At low frequencies, XC2 in parallel with RE creates an impedance that reduces the voltage gain. Figure 15 Development of the equivalent bypass RC circuit. Figure 16 Total Low Frequency Response of Amplifier Composite Bode plot of a BJT amplifier response for three lowfrequency RC circuits with different critical frequencies. Total response is shown by the blue curve. Figure 17 Composite Bode plot of an amplifier response where all RC circuits have the same fc. (Blue is ideal; red is actual.) Figure 18 High Frequency Response of BJT Amplifiers Coupling & bypass capacitors: effective shorts Internal capacitance: significant ONLY at high frequencies Capacitively coupled amplifier and its high-frequency equivalent circuit. Figure 19 High-frequency equivalent circuit after applying Miller’s theorem. Cin( Miller) C bc Av 1 Cout( Miller) Av 1 Cbc Av Figure 20 Development of the equivalent high-frequency input RC circuit. X Ctot RS // R1 // R2 // ac re' 1 2f cu (input) Ctot f cu (input) RS // R1 // R2 // ac re' 1 2 ( RS // R1 // R2 // ac re' )C tot Figure 21 Example: Derive the equivalent high-frequency input RC circuit for the BJT Amplifier in Figure 22 Figure 22 Development of the equivalent high-frequency output RC circuit. Figure 24 High-frequency Bode plots. Figure 26 A BJT amplifier and its generalized ideal response curve (Bode plot). Figure 27