Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Understanding Differential Gain (A_d)
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Let's start by discussing differential gain, denoted as A_d. Can anyone explain what differential gain represents in the context of amplifiers?
I think it’s how much the amplifier increases the voltage difference between two input signals.
Correct! The differential gain, A_d, measures how effectively our amplifier amplifies the input difference. It’s given by the formula, A_d = -g_mR_C/2. What does g_m represent?
G_m is the transconductance of the transistor.
Exactly! Transconductance is a measure of how much output current changes per unit input voltage change. Now, can someone remind me the typical value of V_T at room temperature?
It’s approximately 26 mV.
Great! So for a practical example, if you have a collector resistor R_C of 4.7kΩ and a quiescent collector current of 0.5 mA, how would we calculate A_d?
We’d plug in the values into A_d = -g_mR_C/2, using g_m = (0.5 mA)/26 mV.
Very well put! Let’s summarize today's session: Differential gain quantifies voltage amplification of input signals and relies on key parameters like transconductance and collector resistance. Keep practicing the calculations to strengthen your understanding!
Calculating Common-Mode Gain (A_cm)
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Now that we've grasped A_d, let’s move on to common-mode gain, A_cm. Who can explain what A_cm measures?
I believe it measures the output due to a common signal applied to both inputs.
Correct! Ideally, we want A_cm to be very small since it indicates our amplifier's response to unwanted signals. The formula we use is A_cm = -R_C/(2R_E). What happens if R_E is large?
If R_E is high, A_cm becomes smaller, which is what we want!
Exactly, larger R_E enhances the common-mode rejection. Now, let's dive into calculating A_cm in a scenario. If R_C is 4.7 kΩ and R_E is 100 kΩ, can someone calculate A_cm?
So, it would be A_cm = -4.7kΩ / (2 x 100kΩ), which gives A_cm = -0.0235.
Correct! This is a very small common-mode gain, indicating good performance. Summarizing, common-mode gain is crucial for rejecting noise, and large emitter resistors help minimize this gain.
Understanding CMRR
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Let’s discuss the Common Mode Rejection Ratio, or CMRR. Why do you think CMRR is important in amplifiers?
It shows how well the amplifier can reject common signals while amplifying the differential signal.
Exactly! CMRR is defined as the ratio of the absolute values of differential gain to common-mode gain. The formula is CMRR = |A_d| / |A_cm|. If we have A_d of -45.19 and A_cm of -0.0235, how would we calculate CMRR?
We’d divide the absolute values: CMRR = 45.19 / 0.0235.
Very well! What can we conclude from a high CMRR value?
It indicates better noise rejection in the amplifier, making it more effective in real applications.
Absolutely! To summarize, a high CMRR enhances performance by allowing differential signals to pass through while blocking common-mode noise effectively.
Calculating Input Common Mode Range (ICMR)
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Now we will delve into the Input Common Mode Range, or ICMR. What do you understand about this concept?
It’s the range of input voltages where the amplifier still operates linearly.
Right! If the input voltages go beyond this range, what happens to the output?
The output may cut off or saturate, affecting the amplifier's linear operation.
Exactly! The ICMR is usually constrained by the cutoff and saturation of the transistors. Why do you think we need to know the ICMR in practical applications?
It helps ensure that the amplifier will work correctly under realistic operating conditions, avoiding distortion.
Well-observed! To summarize, ICMR indicates voltage boundaries for valid input signals, ensuring the reliable performance of the amplifier in real circuits.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The section emphasizes the calculation of differential gain, common-mode gain, Common Mode Rejection Ratio (CMRR), and Input Common Mode Range (ICMR) in a BJT differential amplifier setup, detailing formulas and examples to guide students through each calculation.
Detailed
BJT Differential Amplifier Calculations
In this section, we dive deeper into the mathematical aspects of the BJT differential amplifier, which is key in many analog applications. We focus on several vital performance metrics, including the differential gain (D), common-mode gain (_C), Common Mode Rejection Ratio (CMRR), and Input Common Mode Range (ICMR). The following outlines these calculations in detail:
Differential Gain (A_d)
The differential gain quantifies how much the amplifier increases the voltage of a differential input signal. It is defined as:
A_d = _out / _in, where g_m represents the transconductance (G), a measure of how effectively the input signal can control the output current. The key equation for differential gain is:
$$
A_d = -\frac{g_mR_C}{2} = -\frac{I_CQR_C}{2V_T}
$$
where:
- g_m = C / V_T (with V_T typically around 26 mV at room temperature)
- I_C is the quiescent collector current.
Common-Mode Gain (A_cm)
This gain measures the response of the differential amplifier to common-mode signals. Ideally, it should be as low as possible, generally evaluated as:
$$
A_cm = -\frac{R_C}{2R_E}
$$
where R_E may denote the emitter degeneration resistor. A very small value is desired for A_cm to assure good rejection of noise signals common to both inputs.
Common Mode Rejection Ratio (CMRR)
Critical for assessing the effectiveness of a differential amplifier is the CMRR, defined as:
$$
CMRR = \frac{\lvert A_d \rvert}{\lvert A_cm \rvert}
CMRR ext{ (in dB)} = 20log_{10}\left(\frac{\lvert A_d \rvert}{\lvert A_cm \rvert}\right)
$$
A high CMRR signifies that the amplifier skillfully rejects common-mode signals while effectively amplifying the intended differential input.
Input Common Mode Range (ICMR)
Finally, the ICMR indicates the range of common-mode input signals for which the amplifier can operate linearly without saturation or cutoff. Understanding ICMR is critical for practical applications, ensuring that the amplifier can handle real-world signal variations. Typically, ICMR is constrained by the transistors entering cutoff or saturation at extreme input supply levels.
Through these calculations, students will gain a clear insight into how theoretical values predict and guide real-life amplifier performance, fostering a deeper understanding of BJT differential amplifiers.
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Differential Gain Calculation (A_d)
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Calculate I_CQ (quiescent collector current per transistor, from 7.1).
Calculate Transconductance (g_m=I_CQ/V_T, where V_T=26mV).
A_d=−g_mR_C/2 = [Your Calculation]
Detailed Explanation
To calculate the differential gain (A_d) of the BJT differential amplifier, we first need to find the quiescent collector current (I_CQ) for each of the transistors in the circuit. This current is essential because it's the current operating through the transistors under no signal input. After we determine this value, we can calculate the transconductance (g_m), which determines how effectively the transistors can amplify the input signal. Transconductance is calculated using the formula g_m = I_CQ / V_T, where V_T, typically at room temperature, is approximately 26mV. Finally, we combine these results to compute the differential gain using A_d = -g_mR_C/2, where R_C is the collector resistor.
Examples & Analogies
Think of the differential gain as how loud a voice can be amplified based on how strong the original whisper (current) is and how powerful the speaker (resistor) is within an amplifier. The stronger your whisper (I_CQ), the more loudly the speaker can reproduce that sound (A_d). Similarly, in everyday tasks, if you have a strong foundation (current), tools at hand (resistors), and know how to use them, you'll amplify your effort effectively.
Common-Mode Gain Calculation (A_cm)
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
If using resistor R_E for current source: A_cm=−R_C/2R_E = [Your Calculation]
If using BJT current source: (This formula is more complex, involving output resistance of current source, r_o. Often, A_cm is primarily determined experimentally due to high output resistance.)
Detailed Explanation
The common-mode gain (A_cm) refers to the amplifier's response when the same input signal is applied to both transistors. In sensor circuits, this is crucial as outside noise can affect both signals equally. If we are utilizing a resistor (R_E) as our current source, we calculate the common-mode gain using the formula A_cm = -R_C / (2R_E), which highlights the relationship between the collector resistance and the emitter resistor. If instead, we use a bipolar junction transistor (BJT) as our current source, the calculation becomes more complex due to other factors such as the output resistance of that transistor, denoted as r_o. In such cases, common-mode gain is often determined experimentally rather than through straightforward calculations.
Examples & Analogies
Imagine you are trying to hear a conversation while construction is happening nearby. If both your ears hear the same loud construction noise (common mode input), your brain would struggle to discern the actual conversation (differential output). The gain you hear from the construction noise reflects how well your ear can mitigate the background noise. In electronics, the common-mode gain reflects this scenario, where the circuit struggles to minimize equal inputs from both paths and focuses on finding the actual different signal.
CMRR Calculation
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
CMRR=|A_d|/|A_cm| (using measured values from 7.2) = [Your Calculation]
CMRR_dB=20log_10(CMRR) = [Your Calculation] dB
Detailed Explanation
The Common-Mode Rejection Ratio (CMRR) is a critical parameter that represents how well the differential amplifier can reject common-mode signals while amplifying the desired differential signals. It is calculated by taking the absolute values of the differential gain (|A_d|) and common-mode gain (|A_cm|) and forming a ratio. The larger this ratio is, the better the amplifier is at rejecting unwanted noise or interference that can skew the signal. The CMRR can also be expressed in decibels (dB) using the formula CMRR_dB = 20 * log_10(CMRR), which provides a more manageable scale to comprehend the performance of the amplifier.
Examples & Analogies
Consider CMRR like having a filter that separates good music from background noise at a concert. If that filter works exceptionally well, it lets you enjoy the music while blocking out the noise; in technical terms, a high CMRR setup does exactly the same by minimizing common-mode interference, allowing only the desired signals to be amplified and heard.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Differential Gain (A_d): Indicates how much the amplifier increases the voltage difference between input signals.
-
Common-Mode Gain (A_cm): Measures the amplifier's output for identical input signals applied to both inputs.
-
Common Mode Rejection Ratio (CMRR): Reflects the ability of the amplifier to reject common-mode interference while amplifying desired signals.
-
Input Common Mode Range (ICMR): Defines the range of common-mode input signals for which the amplifier operates linearly.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
Suppose you design a BJT differential amplifier with R_C = 4.7 kΩ and I_CQ = 0.5 mA. The differential gain would be calculated as A_d = -[(0.5 mA) * (4.7 kΩ)] / (2 * 26 mV) = -45.19.
-
If you have a common-mode gain calculation where R_E = 100 kΩ and R_C = 4.7 kΩ, A_cm = -4.7 kΩ / (2 * 100 kΩ) gives A_cm = -0.0235, indicating a strong resistor configuration.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
Differential gain shines like gold, amplifying tales yet untold. Common mode gain, keep it low, helps the signal well to flow.
📖 Fascinating Stories
-
Imagine a storyteller, amplifying two distinct tales. The differential gain amplifies the difference, while the common-mode tells a quieter, unified story to reject noise.
🧠 Other Memory Gems
-
Remember 'DC' for Differential Gain is where C means collector, the D for difference.
🎯 Super Acronyms
Acronym CMRR to Recall
- C: = Common
- M: = Mode
- R: = Rejection
- R: = Ratio
- for clarity on this measure.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Differential Gain (A_d)
Definition:
The factor by which a differential amplifier increases the amplitude of the difference between two input signals.
-
Term: CommonMode Gain (A_cm)
Definition:
The gain of a differential amplifier when the same signal is applied to both input terminals.
-
Term: Common Mode Rejection Ratio (CMRR)
Definition:
A measure of a differential amplifier's ability to reject common-mode signals; calculated as the ratio of the absolute values of differential gain and common-mode gain.
-
Term: Input Common Mode Range (ICMR)
Definition:
The range of common-mode input voltages over which the differential amplifier can operate linearly without saturation or cutoff.
-
Term: Transconductance (g_m)
Definition:
The ratio of output current to input voltage change, indicating the effectiveness of an amplifier stage.
-
Term: Quiescent Collector Current (I_CQ)
Definition:
The steady-state current flowing through a transistor when no input signal is applied.