Enrol to start learning
Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.
80.1.5. Common Mode Gain Calculation
Interactive Audio Lesson
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free account
Today, we'll discuss the differential amplifier's unique functionality, particularly focusing on common mode gain. Who can tell me what a differential amplifier does?
It amplifies the difference between two input signals.
Exactly! And why is that useful?
It's useful because it helps cancel out noise and common signals that are the same at both inputs.
Correct! This is a fundamental trait of differential amplifiers, and today we will see how this trait can be quantified with common mode gain.
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free account
Let’s define common mode gain. What is common mode gain in the context of a differential amplifier?
Is it the gain produced when both inputs of the amplifier receive the same signal?
Exactly! Common mode gain helps us understand how effectively an amplifier can reject signals that are present on both inputs. What formula can we use to calculate it?
I think it’s something like A_{cm} = -\frac{g_m R}{1 + 2g_m r_o}?
Great job! Let's break down this equation for clarity. Here, is the transconductance and is the output resistance. This will be important when we look at practical scenarios.
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free accountNow, let’s delve into calculating common mode gain with our differential amplifier configured with MOSFETs and BJTs. What parameters do we need?
We need the transconductance, resistance values, and the output resistance.
Absolutely! An example to reinforce our understanding: if we have and , what can we derive?
We could substitute these values into the formula to find the common mode gain.
Exactly right! And remember, by using an active device like a BJT instead of a passive resistor, we can improve our gain performance.
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free accountNow, let’s consider the impact of replacing passive elements with active elements. How does this affect common mode gain?
Active devices can provide a more stable current source, resulting in better control of output signals.
Exactly! Also, they help suppress common mode signals while ensuring the output remains primarily the differential signal. Any thoughts on practical applications of this?
Using this in audio equipment could really enhance sound quality!
Certainly! This is why understanding common mode gain is crucial in designing high-fidelity audio systems. Let's summarize what we've learned today.
Overview
Short Summary
This section discusses the calculation of common mode gain in a differential amplifier that combines MOSFETs and BJTs.
Medium Summary
The section elaborates on how to calculate the common mode gain in a differential amplifier configured with both BJTs and MOSFETs. It explains the importance of using active devices to improve circuit performance and decrease unwanted common mode signals while maintaining the integrity of differential signals.
Detailed Summary
Common Mode Gain Calculation
In this section, we focus on the calculation of common mode gain in a differential amplifier that utilizes both MOSFET and BJT devices. The introduction of an active device instead of a passive tail resistor significantly enhances circuit performance. The common mode gain is calculated using specific formulas accounting for parameters such as transconductance and input resistance. We demonstrate how the input common mode voltage range is defined by the circuit configuration, discussing the implications of this range on the operating point of the transistors involved. Specifically, we derive the formula for common mode gain as:
where is the transconductance, is the resistance, and is the output resistance. We also derive examples to illustrate these calculations, highlight the ramifications of active devices in suppressing common mode signals, and confirm the relationship between differential and common mode signals in practical applications.
Reference YouTube Videos
Audio Book
Unlock the audio lesson
The script is above and free to read. A free account plays it back, in the voice you pick.
Create a free accountSo we do have a differential amplifier and also I must say that in this circuit this is the first time we are trying to combine both MOSFET and BJTs together within one amplifier, and this is of course intentional just to give you a confidence that you can mix BJT as well as MOS in a, in your circuit.
Detailed Explanation
This part introduces the concept of a differential amplifier that combines MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors) and BJTs (Bipolar Junction Transistors). This combination is strategic; it shows students that they can integrate different types of transistors within a single circuit design, leveraging the strengths of each type as long as proper guidelines are followed.
Examples & Analogies
Imagine a chef making a new recipe by mixing ingredients from different cuisines. Just as the chef expertly blends flavors and techniques to create a delicious dish, engineers mix different transistor technologies to achieve optimal performance in electronic circuits.
Unlock the audio lesson
The script is above and free to read. A free account plays it back, in the voice you pick.
Create a free accountIn fact, if you see the device characteristic you may see that it is almost working as one ideal current source but it may be having some finite conductance. And this conductance sorry inverse of this conductance is basically r_o1...
Detailed Explanation
This section explains how the biasing is set up in the amplifier circuit. By considering base biasing values (like R1 = 570 kΩ and V_BE = 0.6 V), the section calculates the expected current outputs (e.g., I = 20 µA and then I = 2 mA from β = 100). It also emphasizes the symmetry of the circuit as both branches have equal currents. This illustrates how precise biasing ensures consistent performance across transistors.
Examples & Analogies
Think of a balanced scale where both sides need to hold the same weight for it to stay level. The calculated currents in the differential amplifier are like the weights on the scale – having them balanced allows the circuit to perform effectively.
Unlock the audio lesson
The script is above and free to read. A free account plays it back, in the voice you pick.
Create a free accountSo, in summary what we can say that V_INC, V_INC is having a nice range, the upper limit it is 9 V and lower limit it is 2.3 V...
Detailed Explanation
The common mode input voltage defines the range within which the voltage can vary without affecting the performance of the amplifier. It discusses the limits (2.3 V and 9 V) and how these may vary depending on design choices like current settings and resistor values. Understanding these limits is crucial for ensuring that the circuit operates properly without entering undesirable states such as saturation.
Examples & Analogies
Think of a comfortable temperature range in a room. Just like you'd adjust the thermostat to keep the temperature between certain limits (neither too hot nor too cold), engineers set input common mode voltage limits to ensure the amplifier functions optimally.
Unlock the audio lesson
The script is above and free to read. A free account plays it back, in the voice you pick.
Create a free accountSo, to calculate the common mode gain we know that the in the expression of common mode gain we do have g_m × R_D and in the denominator we do have (1 + 2g_m r_o1)...
Detailed Explanation
This segment provides the formula for calculating common mode gain, representing how the circuit responds to signals that affect both inputs equally. It highlights the key role played by transconductance (g_m) and the output resistance (r_o1) in determining this gain. The significance of using an active tail device instead of a passive element is also emphasized to enhance performance.
Examples & Analogies
Consider a rubber band that stretches to let in light while keeping darkness out. Just like the band needs to handle pressure evenly to deliver light smoothly, amplifiers need to manage common mode signals effectively to maintain clear outputs without distortion.
Unlock the audio lesson
The script is above and free to read. A free account plays it back, in the voice you pick.
Create a free accountIn fact, by replacing this passive element by this active device since, now we are getting common mode gain it is –g_m R_D...
Detailed Explanation
This section elaborates on how the use of an active device instead of a passive one significantly improves the common mode gain calculation. This improvement leads to better suppression of unwanted common mode signals, allowing the differential signal to dominate, resulting in clearer output signals.
Examples & Analogies
This is akin to using a powerful filter to clean water. Just as a robust filter can remove impurities and provide clean drinking water, implementing active devices in circuits allows for the filtering out of noise and interference, improving the quality of the output signals.
--
Key Concepts
Core takeaways and short definitions to help you quickly recall the key ideas from this section.
Differential Amplifier: Amplifies the difference between two signals.
Common Mode Gain: The amplification of signals that are common to both inputs.
Active Device: A circuit component that can control the flow of electricity.
Examples
Step-by-step examples to apply the section's ideas and test your understanding.
When the same input signal is applied to both terminals of a differential amplifier, the common mode gain is calculated to ascertain how much amplification occurs.
Using a BJT as an active tail resistor in a differential amplifier can provide higher common mode rejection.
Memory Aids
Interactive tools to help you remember key concepts
Stories
Memory Tools
Flash Cards
Glossary
Differential Amplifier
An amplifier that amplifies the difference between two input signals while rejecting common signals.
Common Mode Gain
The gain of an amplifier when the same signal is applied to both inputs.
Transconductance (gm)
The ratio of the output current to the input voltage in a transistor.
BJT
Bipolar Junction Transistor, a type of transistor that uses both electron and hole charge carriers.
MOSFET
Metal-Oxide-Semiconductor Field-Effect Transistor, a type of transistor used for amplifying or switching electronic signals.
Early Voltage
A parameter that quantifies the output resistance of a transistor, affecting its transconductance.