Frequency: Miller, cascode, cascade
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| coupling capacitor | tụ ghép |
| Miller capacitance | điện dung Miller |
| dominant pole | cực chi phối |
Frequency: Miller, cascode, cascade
- The low corner: each coupling capacitor against the resistance it sees with sources zeroed, $f_L = 1/(2\pi R_{eq}C)$. The high corner: Miller capacitance — a capacitor $C$ across a stage of gain $-A$ behaves at the input as $C(1+A)$ — under the dominant-pole rule $f_H = 1/(2\pi R_{eq}C_{eq})$.
- The cascode kills the gain across the capacitor and reclaims the bandwidth; the cascade (stages in series) shrinks corners by $\sqrt{2^{1/n} - 1}$ per stage added.
The CE stage: coupling sees $R_B \parallel r_\pi = 2.08$ kΩ, so 10 µF gives $f_L = 7.7$ Hz. Miller: 5 pF across a −80 stage becomes $405$ pF; with 20 pF stray, $f_H = 187$ kHz. Cascode (Miller killed): $1/(2\pi \times 2\mathrm{k} \times 25\mathrm{p}) = 3.18$ MHz — 17×. Two cascaded 187 kHz stages: −3 dB at $187 \times \sqrt{2^{1/2} - 1} = 120$ kHz.

{exercise:uni-ee5x-frequency}
A 5 pF capacitor across a stage of gain -80 makes the input see
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Miller: C_M = C(1 + |A|) = 5 x 81 = 405 pF. The capacitor sees the input AND the opposite-moving output - the current is (1+A) times.
With 405 pF Miller + 20 pF stray on a 2 kOhm node, fH is about
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fH = 1/(2pi x 2k x 425p) = 187 kHz. A cascode kills the Miller term: 25 pF gives 3.18 MHz - 17x for one transistor.
Two identical 187 kHz stages cascaded have an overall -3 dB corner at
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Each stage is -3 dB at its corner, so the pair is -6 dB there; the overall -3 dB sits at 187 x 0.644 = 120 kHz.