) Below is the small signal model of a multistage amplifier. Using this mo del, write the equationsthat you would need to determine the voltagegain. IMPORTANT: You only need to provide the equationsthat you would need to determinethe voltage gain. You DO NOT need to combine and simplify the equations to determine a final expression for the voltagegain. Vin Vo Vo1 Rb R12 Vbe1 Vbe2 e gm 1 Vbe1 Rc1 gm 2 Vbe2 Rc2 Re

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### Multistage Amplifier Small Signal Model

Below is the small signal model of a multistage amplifier. Using this model, write the equations that you would need to determine the voltage gain.

#### Important: 
- You only need to provide the equations needed to determine the voltage gain.
- You **DO NOT** need to combine and simplify these equations into a final expression for the voltage gain.

#### Circuit Description:

- **Vin to Vo:**
  - The input voltage is labeled as \( V_{in} \), and the output voltage is labeled as \( V_o \).

- **Components:**
  - **R1, R_b:** Resistors connected to the base.
  - **r'1, r'2:** Small signal resistances equivalent for the transistors.
  - **R_c1, R_c2:** Collector resistors.
  - **R_e:** Emitter resistor.
  - **gm1 vbe1, gm2 vbe2:** Transconductance components for each transistor stage.

- **Nodes:**
  - **Vb, Va, Vo1:** Intermediate voltages across different stages.

#### Model Stages:

1. **First Stage:**
   - Transistor input: \( V_{be1} = V_b - Va \)
   - Output influenced by transconductance: \( gm_1 v_{be1} \)
   
2. **Second Stage:**
   - Transistor input: \( V_{be2} = Vo_1 - Vo \)
   - Output influenced by transconductance: \( gm_2 v_{be2} \)

3. **Equations:**
   - Determine expressions for each \( V_{be} \) across stages using Ohm’s Law and equivalent resistances.
   - Write the output expressions for each stage using \( I_c = gm \times V_{be} \) multiplied by the respective \( R_c \).

By logically analyzing each stage and their contributions, the overall voltage gain can be calculated by cascading the voltage gains of each individual stage. Remember, combining and simplifying into a final formula is not required here.
Transcribed Image Text:### Multistage Amplifier Small Signal Model Below is the small signal model of a multistage amplifier. Using this model, write the equations that you would need to determine the voltage gain. #### Important: - You only need to provide the equations needed to determine the voltage gain. - You **DO NOT** need to combine and simplify these equations into a final expression for the voltage gain. #### Circuit Description: - **Vin to Vo:** - The input voltage is labeled as \( V_{in} \), and the output voltage is labeled as \( V_o \). - **Components:** - **R1, R_b:** Resistors connected to the base. - **r'1, r'2:** Small signal resistances equivalent for the transistors. - **R_c1, R_c2:** Collector resistors. - **R_e:** Emitter resistor. - **gm1 vbe1, gm2 vbe2:** Transconductance components for each transistor stage. - **Nodes:** - **Vb, Va, Vo1:** Intermediate voltages across different stages. #### Model Stages: 1. **First Stage:** - Transistor input: \( V_{be1} = V_b - Va \) - Output influenced by transconductance: \( gm_1 v_{be1} \) 2. **Second Stage:** - Transistor input: \( V_{be2} = Vo_1 - Vo \) - Output influenced by transconductance: \( gm_2 v_{be2} \) 3. **Equations:** - Determine expressions for each \( V_{be} \) across stages using Ohm’s Law and equivalent resistances. - Write the output expressions for each stage using \( I_c = gm \times V_{be} \) multiplied by the respective \( R_c \). By logically analyzing each stage and their contributions, the overall voltage gain can be calculated by cascading the voltage gains of each individual stage. Remember, combining and simplifying into a final formula is not required here.
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