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Razavi 电子电路 1

该笔记用于记录学习 Razavi Electronics Circuits 1

信号的完成性和匹配 Signal Integrity and Matching

Why do we need to analysis input and output impedance in analog circuit?

  • Input Impedance: The input impedance of a circuit determines how much of the input signal is absorbed by the circuit. If the input impedance is too low compared to the source impedance(源阻抗), a significant portion of the signal will be lost, leading to signal attenuation.

  • Output Impedance: The output impedance affects how the circuit drives a load (负载). If the ouput impedance is not well-matched to the load impedance, signal reflection or losses can occur, especially in high-frequency application.

  • Impdance Matching: In many analog cirits, especially in RF and audio aplications, impedae matching is essential to ensure maximum power transfer and mnimize reflections.

Thevenin equivalent 戴南维等式

Alternative analysis

  1. Determine Vth (Thevenin voltage):

    • Remove the load resistor from the original circuit.
    • Calculate the open-circuit voltage across the terminals where the load was connected. This is Vth.

  2. Determine Rth (Thevenin resistance):

    • Remove all voltage sources (replace them with short circuits) and current sources (replace them with open circuits).
    • Calculate the equivalent resistance seen from the load terminals. This is Rth.

  3. Rebuild the circuit:

    • Once you have Vth and Rth, you can draw the Thevenin equivalent circuit with Vth in series with Rth, and the load resistor connected to them.

退化电阻对于共射极(BJT)和共源极(MOSFET)的影响

无退化电阻时的增益推导

  1. 共射极放大器BJT (CE without \(R_E\)):

    • Without Early effect: $$ A_v = -g_m R_C $$
    • With Early effect: $$ A_v = -g_m \left(R_C \parallel r_o\right) $$

  2. 共源极放大器MOSFET (CS without $R_S):

    • Without Channel Length Modulation: $$ A_v = -g_m R_D $$
    • With Channel Length Modulation: $$ A_v = -g_m (R_D \parallel r_o) $$

有退化电阻时的增益推导

  1. 共射极放大器BJT (CE with \(R_E\)):

    • Without Early effect: $$ A_v = -\frac{g_m R_C}{1 + g_m R_E} $$
    • With Early effect: $$ A_v = -\frac{g_m (R_C \parallel r_o)}{1 + g_m R_E} $$

  2. 共源极放大器MOSFET (CS with $R_S):

    • Without Channel Length Modulation: $$ A_v = -\frac{g_m R_D}{1 + g_m R_S} $$
    • With Channel Length Modulation: $$ A_v = -\frac{g_m (R_D \parallel r_o)}{1 + g_m R_S} $$

These expressions often ignore \(r_o\) (output resistance), and here's why.

Why Is \(r_o\) Often Ignored with Degeneration?

Reasons

  1. Degeneration introduces local feedback, increasing output impedance and reducing the influence of \(r_o\).

  2. Simplifies design and teaching — textbooks often omit second-order effects in first-pass analysis.

  3. r_o is typically large, making its impact negligible in many practical cases:

  4. BJT: $$ r_o = \frac{V_A}{I_C} $$
  5. MOSFET: $$ r_o = \frac{1}{\lambda I_D} $$

忽略 \(r_o\) 是一种建模简化，适用于初步分析和大多数设计情况。对于高精度设计、宽带电路或高阻负载时，必须考虑 \(r_o\)（Early effect 或 Channel Length Modulation） 的影响。