Assume gm = 5 mA/V and ro= 20k 2. Using the short-circuit time constants approach, which of the coupling capacitors causes the dominant pole in the lov frequency response of the amplifier? Vsig Rsig = 200 ΚΩ www RGI 2 ΜΩ· HH CC1 = 0.1 µF RG2 ΙΜΩ VDD Rs 2 ΚΩ RD 10 ΚΩ 2₁ ww HH Cc2= 0.1 µF Cs=5 µF -OV₂ Rz = 10 ΚΩ

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**Educational Explanation: Amplifier Circuit Analysis**

**Problem Statement:**
Assume \( g_m = 5 \, \text{mA/V} \) and \( r_o = 20k \, \Omega \). Using the short-circuit time constants approach, determine which of the coupling capacitors causes the dominant pole in the low-frequency response of the amplifier.

**Circuit Description:**
The provided circuit diagram is a common-source amplifier with the following components and values:

- \( R_{\text{sig}} = 200 \, \text{k}\Omega \): Signal source resistance.
- \( R_G1 = 2 \, \text{M}\Omega \) and \( R_G2 = 1 \, \text{M}\Omega \): Gate resistors.
- \( C_1 = 0.1 \, \mu\text{F} \) and \( C_2 = 0.1 \, \mu\text{F} \): Coupling capacitors.
- \( R_S = 2 \, \text{k}\Omega \): Source resistor.
- \( C_S = 5 \, \mu\text{F} \): Bypass capacitor.
- \( R_D = 10 \, \text{k}\Omega \): Drain resistor.
- \( R_L = 10 \, \text{k}\Omega \): Load resistor.
- \( Q_1 \): Transistor with given \( g_m \) and \( r_o \).
- \( V_{\text{DD}} \): Power supply voltage.
- Input signal \( V_{\text{sig}} \) connected to the gate.

**Task:**
Evaluate the effect of each capacitor on the low-frequency response using the short-circuit time constants method, and identify which capacitor sets the dominant pole.

**Answer Options:**
- \( C_1 \)
- \( C_2 \)
- \( C_{gd} \) (Gate-drain capacitance, not explicitly shown)
- \( C_S \)

**Approach:**
1. Recognize that the dominant pole is the one with the largest time constant (RC value) and thus, affects the bandwidth significantly.
2. Analyze the reactance of each capacitor at low frequencies to determine which has the most significant impact. 

This challenge requires understanding of frequency response and RC charging circuits in amplifiers.
Transcribed Image Text:**Educational Explanation: Amplifier Circuit Analysis** **Problem Statement:** Assume \( g_m = 5 \, \text{mA/V} \) and \( r_o = 20k \, \Omega \). Using the short-circuit time constants approach, determine which of the coupling capacitors causes the dominant pole in the low-frequency response of the amplifier. **Circuit Description:** The provided circuit diagram is a common-source amplifier with the following components and values: - \( R_{\text{sig}} = 200 \, \text{k}\Omega \): Signal source resistance. - \( R_G1 = 2 \, \text{M}\Omega \) and \( R_G2 = 1 \, \text{M}\Omega \): Gate resistors. - \( C_1 = 0.1 \, \mu\text{F} \) and \( C_2 = 0.1 \, \mu\text{F} \): Coupling capacitors. - \( R_S = 2 \, \text{k}\Omega \): Source resistor. - \( C_S = 5 \, \mu\text{F} \): Bypass capacitor. - \( R_D = 10 \, \text{k}\Omega \): Drain resistor. - \( R_L = 10 \, \text{k}\Omega \): Load resistor. - \( Q_1 \): Transistor with given \( g_m \) and \( r_o \). - \( V_{\text{DD}} \): Power supply voltage. - Input signal \( V_{\text{sig}} \) connected to the gate. **Task:** Evaluate the effect of each capacitor on the low-frequency response using the short-circuit time constants method, and identify which capacitor sets the dominant pole. **Answer Options:** - \( C_1 \) - \( C_2 \) - \( C_{gd} \) (Gate-drain capacitance, not explicitly shown) - \( C_S \) **Approach:** 1. Recognize that the dominant pole is the one with the largest time constant (RC value) and thus, affects the bandwidth significantly. 2. Analyze the reactance of each capacitor at low frequencies to determine which has the most significant impact. This challenge requires understanding of frequency response and RC charging circuits in amplifiers.
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