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The maximum current flows when |X C | << R In other words, the capacitor couples the signal properly when |X C | << R The size of the coupling capacitor.

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Presentation on theme: "The maximum current flows when |X C | << R In other words, the capacitor couples the signal properly when |X C | << R The size of the coupling capacitor."— Presentation transcript:

1 The maximum current flows when |X C | << R In other words, the capacitor couples the signal properly when |X C | << R The size of the coupling capacitor depends on the lowest frequency you are trying to couple, because |X C | increases when frequency decreases. We will use the rule T = RC (eqn. 2) at the lowest freq. (T = 1/f). (All other freq. will be well coupled.) Coupling and Bypass Capacitors Coupling Capacitor: -passes a signal from one ungrounded point to another ungrounded point. (Not practical for IC’s therefore IC amplifiers are usually direct coupled.) (eqn.1)

2 Coupling and Bypass Capacitors Example: To couple freq. in the range 20 Hz to 50kHz. The lowest freq. = 20 Hz  T = 1/20 = 0.05 sec If the total resistance in a one loop circuit is 10k , the coupling capacitor must satisfy T = RC. 0.05 = 10k X C  C = 0.05/10k = 5  F Another widely used rule is to keep |X C | < (1/10) R Bypass Capacitor: -similar to coupling capacitor except it couples an ungrounded point to a grounded point. Eqns. (1) and (2) still apply. In this case 

3 Coupling and Bypass Capacitors Example: The input signal in the Figure can have a frequency between 10Hz and 50khz. Find the size of the coupling capacitor. Example: We want an AC ground on point A in the Figure. Find the size of the bypass capacitor   24k | |12k = 8k and Thevenize cct. to the left of the capacitor R TH =2k for the lowest freq. We need at least 800  F

4 AC Equivalent Circuits and Frequency Response Up until now all of the small-signal AC equivalent circuits we have used have been mid-frequency band models. Low-frequency AC Equivalent Circuit CE Amplifier Fig. 7.14 p. 609  mid-frequency  low-frequency high-frequency

5 AC Equivalent Circuits and Frequency Response We will use a simplified analysis approach. (An exact analysis could be done using SPICE) To determine  L, the lower 3db frequency: First set V s to zero, C E and C C2 to infinity and find the resistance R C1 seen by C C1. R C1 = R S + [R B || (r x + r  )] Next set C C1 and C C2 to infinity and determine the resistance R’ E seen by C E Set both C C1 and C E to infinity and find the resistance seen by C C2 R C2 = R L + (R C || r o) An approximate value for the lower 3db freq. can now be found now that the equivalent RC time constants are known.

6 High–frequency model for CE Amplifier (a) High –Freq. Model (CE) (b) Simplified circuit (Thevenin theorem)

7 This circuit can be further simplified using Miller’s theorem. In our case and Thus Can be replaced by a capacitor connected from terminal B’ to ground. B’ Notice that the input forms a simple RC low-pass filter. The break freq. is given by where is the total capacitance in the input loop. Above f H the gain of the amplifier rolls off at 20 db/decade.

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9 Example: CE Amplifier The hybrid pi parameters are: Also In the high-freq. equivalent circuit model we have:

10 SPICE simulation result


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