Pre-Lab Design and Calculations - 5 | Experiment No. 4: Multistage Amplifiers and Cascode Configuration | Analog Circuit Lab
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5 - Pre-Lab Design and Calculations

Practice

Interactive Audio Lesson

Listen to a student-teacher conversation explaining the topic in a relatable way.

Introduction to Multistage Amplifiers

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0:00
Teacher
Teacher

Today, we are diving into multistage amplifiers. Can anyone tell me why we might use multiple amplifier stages instead of just one?

Student 1
Student 1

To get higher gain!

Student 2
Student 2

And to match input and output impedances.

Teacher
Teacher

Exactly! So, multistage amplifiers help us achieve increased overall gain and better impedance matching. Remember the acronym GAIN: Gain, Amplification, Isolation, and Networking. Those are key benefits!

Types of Coupling

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Teacher
Teacher

Let's talk about how we connect these amplifier stages. We'll start with RC coupling--who can explain what that is?

Student 3
Student 3

It's when we use capacitors and resistors to connect stages, blocking DC but allowing AC signals to pass.

Student 4
Student 4

And it’s cost-effective too!

Teacher
Teacher

Right! Remember, RC coupling not only blocks DC but enhances performance in many applications. Can anyone think of disadvantages?

Student 1
Student 1

It can reduce bandwidth if not designed carefully.

Teacher
Teacher

That's a great observation! The design must balance gain and frequency response.

Cascode Amplifier Design

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0:00
Teacher
Teacher

Now, let’s move to the Cascode amplifier. Why do you think it's designed this way?

Student 2
Student 2

To reduce the Miller effect!

Student 3
Student 3

And improve high-frequency performance!

Teacher
Teacher

Exactly. The Cascode configuration utilizes a common-base stage that provides excellent isolation while maintaining high gain. Can someone summarize how the Cascode configuration addresses the Miller effect?

Student 4
Student 4

It keeps the first stage gain low, which minimizes the effective Miller capacitance.

Teacher
Teacher

Fantastic! The improved frequency response is a major advantage of this design.

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

This section outlines the design and calculation procedures necessary for developing two-stage RC coupled BJT amplifiers and Cascode configurations.

Standard

The section describes the objectives, theoretical background, and apparatus needed for designing two-stage RC coupled BJT amplifiers and Cascode amplifiers, including biasing calculations, component selection, and performance characterization.

Detailed

Detailed Summary

This section focuses on the preparatory steps necessary for executing Experiment No. 4 on Multistage Amplifiers and Cascode Configuration. It begins with outlining the aims and objectives of the experiment, indicating that students will design, construct, and analyze multistage amplifiers, specifically two-stage RC coupled BJT amplifiers and Cascode amplifiers. Several key components are necessary for this experiment, including a regulated power supply, function generator, digital multimeter, and BJT transistors among others.

Theoretical principles related to multistage amplifiers are discussed, emphasizing the need for cascading to achieve desired performance characteristics such as overall voltage gain, bandwidth, and impedance matching for specific applications.

The design process of each stage of the two-stage RC coupled amplifier is elaborated, detailing calculations for biasing configurations using a voltage divider bias scheme, taking into consideration specifications such as supply voltage, transistor parameters, and target quiescent points. Additionally, design steps for the Cascode amplifier are covered, emphasizing how this configuration reduces the Miller effect and improves high-frequency performance. Theoretical Q-points and gains are calculated and listed for both configurations to guide students in their implementation of practical circuits.

Audio Book

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Two-Stage RC Coupled BJT Amplifier Design

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We will design two identical CE stages and then cascade them. Assume biasing will be done using the Voltage Divider Bias scheme (as learned in Experiment 2) for stability.

Detailed Explanation

This chunk outlines the procedure for designing a two-stage amplifier, specifically using two Common-Emitter (CE) stages. The primary focus is on using a Voltage Divider Bias technique, which allows for stable biasing of the transistors in the amplifier. This is critical for ensuring that the amplifier operates efficiently and maintains consistent performance.

Examples & Analogies

Think of this biasing technique like setting the right temperature in a thermostat to ensure your home stays comfortable. Just as you set the thermostat to a specific temperature to maintain a steady environment, the Voltage Divider Bias keeps the transistor operating at an ideal point for amplification.

Common Parameters for Each Stage

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● Supply Voltage: VCC = 12V
● Transistor: NPN BJT (BC547)
● Assume βDC for BC547 = 100
● Assume VBE = 0.7V
● Target Q-point for each stage: IC = 1mA, VCE = 6V

Detailed Explanation

The common parameters specify the operating conditions for the transistor amplifiers. The supply voltage (VCC) is set to 12V, which is the source of power. The transistor type used is an NPN BJT BC547, with a beta (βDC) of 100, indicating the amplification capability. The VBE of 0.7V is a typical voltage drop across the base-emitter junction when the transistor is conducting. The Target Q-point (quiescent point) values are set at IC = 1 mA for the collector current and VCE = 6V for the collector-emitter voltage, ensuring the amplifier operates in its active region.

Examples & Analogies

Consider these parameters like the ingredients and settings for baking a cake. You need the right amounts of flour, sugar, and oven temperature to ensure a delicious cake. Similarly, here, the correct values allow the transistors to function ideally for amplification.

Design for a Single CE Stage

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  1. Target IC = 1mA, VCE = 6V.
  2. Calculate VE and RE :
  3. Let VE ≈ 0.15 × VCC = 0.15 × 12V = 1.8V.
  4. RE = IE VE ≈ IC VE = 1mA × 1.8V = 1.8kΩ.
  5. Choose Standard RE : 1.8kΩ.
  6. Recalculated VE = 1mA × 1.8kΩ = 1.8V.
  7. Calculate VC and RC :
  8. VC = VCE + VE = 6V + 1.8V = 7.8V.
  9. RC = IC (VCC − VC) = 1mA (12V − 7.8V) = 1mA × 4.2V = 4.2kΩ.
  10. Choose Standard RC : 4.2kΩ (or 4.3kΩ for E24 series). Let's use 4.3kΩ.
  11. Recalculated VC = 12V − (1mA × 4.3kΩ) = 12V − 4.3V = 7.7V.
  12. Recalculated VCE = 7.7V − 1.8V = 5.9V. (Close to target 6V).

Detailed Explanation

This section provides a systematic approach to calculating the required resistances and voltages for a single Common-Emitter stage of the amplifier. Starting with the target values for collector current (IC) and collector-emitter voltage (VCE), it calculates the emitter voltage (VE) and the emitter resistor (RE). These values are vital for ensuring proper biasing of the transistor. Next, it calculates the collector voltage (VC) and collector resistor (RC), determining that RC must also meet standard resistor values. The recalculated voltages confirm that they are near the desired values, ensuring that the design meets operational requirements.

Examples & Analogies

Building the circuit is akin to assembling furniture using a manual. Each step has specific measurements and placements to follow, ensuring the final product is stable and functions as intended. Similarly, here, each calculation builds towards an operational amplifier stage.

DC Biasing Summary for Each CE Stage

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● R1 = 82kΩ
● R2 = 22kΩ
● RC = 4.3kΩ
● RE = 1.8kΩ

Detailed Explanation

This summary provides the chosen values for the resistors used in the design of the CE stage. These resistors are pivotal for establishing the DC operating conditions of both the amplifier stages. R1 and R2 form the voltage divider used for biasing the base of the transistor. RC is the collector resistor that affects the output voltage swing, while RE is the emitter resistor which stabilizes the operating point and can also help linearize the amplifier's characteristics.

Examples & Analogies

Imagine a team of athletes where each member specializes in a distinct skill. Each resistor plays its role in the circuit, working together to ensure the amplifier operates smoothly and reliably, just like a team coordinating to win a match.

AC Analysis for a Single CE Stage (Voltage Gain)

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The voltage gain of a CE amplifier is approximately: AV = −re′ RC ∣∣RL Where:
- RC is the collector resistor.
- RL is the effective AC load seen by the collector. For the first stage, RL will be the input impedance of the second stage. For the second stage, RL will be the actual external load (e.g., oscilloscope probe impedance, which is high, or a specified load resistor).
- re′ is the AC emitter resistance, calculated as re′ = IE / 25mV.
- IE ≈ IC = 1mA. So, re′ = 1mA / 25mV = 25Ω.

Detailed Explanation

This section explains how to calculate the voltage gain (AV) of a Common-Emitter amplifier stage. The gain is derived from the collector resistor (RC) and the effective load impedance (RL) seen by the collector. It also highlights that the emitter resistance (re′) plays a crucial role in determining the gain, and describes how to calculate it based on the emitter current. These calculations are vital for predicting how well the amplifier will perform.

Examples & Analogies

Think of voltage gain like volume control on a music system. The output depends on how much you turn up the volume (gain) relative to the input sound (power input). Just like different settings affect the sound differently, in amplifiers, external impedance and resistors shape the overall output.

Coupling Capacitors and Bypass Capacitor

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These capacitors are chosen to have a very low impedance at the operating frequency range. ● CC (Coupling Capacitor): Blocks DC bias from previous/next stages. Its value affects the lower cutoff frequency (fL). Choose a large enough value (e.g., 1μF to 10μF) such that XC is much smaller than the input impedance of the next stage at fL. A common practice is to choose CC such that Rin,stage ≈ 2πfL CC − 1. ● CE (Emitter Bypass Capacitor): Bypasses RE at AC frequencies to prevent negative feedback that would reduce gain. Its value also affects fL. Choose a large enough value (e.g., 10μF to 100μF) such that XCE is much smaller than re′ at fL. A common practice is RE || (re′ + βRin,source ) ≈ 2πfL CE − 1.

Detailed Explanation

This segment discusses the importance of coupling and bypass capacitors in achieving desired frequency responses. The coupling capacitors (CC) are essential for separating the DC bias from AC signals between stages. In contrast, the bypass capacitors (CE) help to maintain amplifier performance by eliminating unnecessary negative feedback at AC frequencies. Both types of capacitors are chosen to ensure they do not introduce significant impedance at the operating frequencies, thereby allowing the amplifier to function effectively.

Examples & Analogies

Consider these capacitors like gatekeepers at a concert. They ensure the right type of crowd (AC signals) gets through while keeping out distractions (DC bias) and preventing crowd noise from affecting the performers (bypass capacitor role).

Gain Calculation for Two-Stage Amplifier

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● Stage 1 Gain (AV1 ):
- Load for Stage 1 is RC in parallel with Rin(stage2).
- RL1(eff) = RC || Rin(stage2) = 4.3kΩ || 2.18kΩ ≈ 1.44kΩ.
- AV1 = −re′ RL1(eff) = −25Ω / 1440Ω = −57.6.
● Stage 2 Gain (AV2 ):
- Load for Stage 2 is RC (assuming high output impedance of oscilloscope as load).
- RL2(eff) = RC = 4.3kΩ.
- AV2 = −re′ RL2(eff) = −25Ω / 4300Ω = −172.
● Overall Gain (AV(total)):
- AV(total) = AV1 × AV2 = (−57.6) × (−172) = 9916.8.
- AV(total),dB = 20log10 (9916.8) ≈ 79.9dB.

Detailed Explanation

In this chunk, the calculation of gains for both stages of the amplifier is presented. The effective load resistances for each stage are calculated, which are crucial for accurately determining the gain. The total voltage gain of the cascaded stages is the product of the individual gains. The results are then expressed in decibels to facilitate easier interpretation of amplification levels, a common practice in audio applications.

Examples & Analogies

Think of the voltage gain like the intensity of sound in a concert hall. Stage 1 amplifies the original sound (input), while Stage 2 increases it further. The two together create a much louder, more powerful performance for the audience, similar to how combined amplifier gains work.

Summary of Components for Two-Stage RC Coupled BJT Amplifier

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● Transistors: Q1, Q2 (BC547)
● Resistors (for each stage):
- R1 = 82kΩ
- R2 = 22kΩ
- RC = 4.3kΩ
- RE = 1.8kΩ
● Capacitors:
- CC1 (Input Coupling) = 1μF
- CC2 (Inter-stage Coupling) = 1μF
- CC3 (Output Coupling) = 1μF (Similar calculation for CC1 but for output load).
- CE1 (Emitter Bypass for Q1) = 10μF
- CE2 (Emitter Bypass for Q2) = 10μF

Detailed Explanation

This section consolidates all the design choices for the two-stage amplifier, listing out all components used, including the transistors, resistors, and capacitors. It acts as a handy reference for building the circuit correctly based on earlier calculations, ensuring each component is matched to the specific design requirements.

Examples & Analogies

Similar to a shopping list for a recipe, this summary lists everything needed for assembling the amplifier. Each component plays a specific role, just as every ingredient is critical to the final dish.

Cascode Amplifier Design Parameters

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Given Parameters:
● Supply Voltage: VCC = 12V
● Transistors: NPN BJT (BC547) - Q1 (CE), Q2 (CB)
● Assume βDC = 100, VBE = 0.7V.
● Let's aim for the same quiescent collector current as the previous stage: IC = 1mA.

Detailed Explanation

This section outlines the foundational parameters needed for designing a Cascode Amplifier. The same supply voltage and transistor type as used in the two-stage amplifier are employed, along with the same beta and base-emitter voltage. Aims to match the collector current from the first stage to maintain consistency in the amplifier's operation.

Examples & Analogies

Think of this like reusing a successful recipe but trying to enhance it with an additional layer. By keeping the foundational ingredients the same, the new design will have a familiar flavor but with improved capabilities.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Voltage Gain: The ratio of output voltage to input voltage in amplifiers.

  • Input and Output Impedance: The resistive effects at the input and output of the amplifier.

  • Bandwidth: The range of frequencies over which the amplifier operates effectively.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • In audio systems, multistage amplifiers are commonly used to achieve high sound quality and amplification.

  • In sensor signal conditioning, RC coupled amplifiers help to prevent loading effects on sensitive sensors.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • To get gain that’s great, don't hesitate; cascade them in a pair, to climb the gain stair.

📖 Fascinating Stories

  • Imagine a tiny voice wanting to shout across a big field; it needs help from multiple friends to reach the other side, much like how amplifiers need support from multiple stages.

🧠 Other Memory Gems

  • Use the acronym 'GAIN' to remember Gain, Amplification, Isolation, Networking.

🎯 Super Acronyms

RC

  • Resistor-Capacitor coupling simplifies the path but blocks direct current.

Flash Cards

Review key concepts with flashcards.

Glossary of Terms

Review the Definitions for terms.

  • Term: Multistage Amplifiers

    Definition:

    Amplifiers that consist of two or more stages connected in cascade to increase overall gain.

  • Term: RC Coupling

    Definition:

    A method of connecting amplifier stages using resistors and capacitors, allowing AC signals to pass while blocking DC.

  • Term: Cascode Amplifier

    Definition:

    An amplifier configuration utilizing both common-emitter and common-base stages to enhance performance, especially at high frequencies.

  • Term: Miller Effect

    Definition:

    A phenomenon that increases the input capacitance of a transistor due to feedback, limiting its gain at high frequencies.