### Multistage Amplifier Small Signal ModelBelow 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.

Given circuit of multistage amplifier

) 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

) 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

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Power Amplifier

The power amplifier is an electronic amplifier designed to maximize the signal strength of a given input. The input signal strength is enhanced to a high enough level to drive output devices such as speakers, headphones, RF (Radio frequency) transmitters, etc. Unlike voltage / current amplifiers, the power amplifier is designed to drive core loads directly and is used as a storage block in the amplifier series.

Maximum Efficiency Criterion

In every field of engineering, there is a tremendous use of the machine and all those machines are equipped for their popular work efficiency so it very much important for operation engineers to monitor the efficiency of the machine, planning engineers to check out the efficiency of the machine before installing the machine and design engineers to design machine for higher efficiency than and then the utility will procure their products that will ultimately lead to profit and loss of the company. It indicates the importance of efficiency right from the initial stage as manufacturing units, intermediate stage as planning coordinators, and end-users stage as a utility.

Question

### 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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