83.4.2.2 - Small Signal Model Analysis for Transistor-2
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Introduction to Current Mirrors
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Good afternoon, class! Today, we're diving into current mirrors. Can anyone tell me what a current mirror is?
Isn't it a circuit that provides a constant current?
And it can replicate that current to other branches too!
Exactly! We can use BJT or MOSFET transistors to build them. The beauty of current mirrors lies in their ability to provide stable biasing in amplifiers.
But how do we analyze these circuits?
That's our next discussion point - we'll cover small signal models for both DC and AC scenarios. Remember, the acronym **'DCAC'**: you track DC conditions and AC signal currents separately.
So, we will start with how the circuit behaves without a signal?
Right! When no signal is present, we focus on the DC setup. Let's explore that in detail.
Small Signal Model: DC Conditions
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Now that we've set the stage, let's analyze the small signal model under DC conditions. What happens to the circuit?
Isn't it open at certain points?
Yes! The DC components lead to an open circuit in our small signal equivalent. This indicates that the voltage across transistors may be zero. Can someone explain why?
Because at DC, there's no AC signal causing a load, right?
Exactly! This means simplifying our analysis considerably. Remember the **'O=Open'** memory aid—open circuits show us where the AC effects don't exist. Anything else about the DC current mirror?
Yeah! When analyzing it, we focus only on the resistances remaining between drain and source.
Correct! Let's summarize: when dealing with DC conditions, we essentially eliminate the passive components unless they're directly affecting our measurements.
Small Signal Model: AC Conditions
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Great job on DC analysis! Now, let’s shift gears to the AC signals. What background knowledge do you think is needed here?
We must consider the input signal currents as they affect the model!
That's right! When an AC signal is applied, we examine the behavior of our current mirror under those conditions. What is the first element we consider?
The voltage dependent current sources?
Absolutely! In the small signal model, these sources need to be characterized properly to predict how they interact with our AC signals.
What's their significance when we analyze performance?
Excellent question! These sources dictate the gain and behavior of the circuit, directly influencing your output based on the input signal. What would be a mnemonic for these components?
Something like **'VCG'** for Voltage Controlled Gain could work!
Perfect! Remember to apply **'VCG'** as you analyze the effect of input signals on the model.
Applications of Current Mirrors
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Now that we've mastered the theoretical aspects, it’s time to explore applications. Where do you see current mirrors being used?
I think they’re used in amplifiers for biasing!
Absolutely! In common emitter and source amplifiers, they are critical. Why do we prefer them over passive resistors?
Because they provide better stability and linearity?
Exactly! They help maintain consistent current flow ensuring better overall performance. Any other applications?
In differential amplifiers as well, right? For biasing and also current mirroring?
Absolutely! They’re ubiquitous in differential circuits due to their efficiency. Let’s wrap up: remember the need for precise matching for current mirrors to function effectively in practical designs.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
The section explains the small signal model of current mirrors in both MOSFET and BJT configurations, describing scenarios where the current mirror carries only DC or signal current. It outlines applications of current mirrors in amplifiers and differential amplifiers, detailing how to analyze these circuits using small signal models.
Detailed
Detailed Summary
In this section, we explore the small signal model analysis for current mirrors using transistors. The discussion begins with the operating principles of current mirrors in analog electronic circuits, followed by a detailed examination of the different configurations such as common emitter and common source amplifiers. The key concepts include:
- Small Signal Equivalent Circuit: Two scenarios are outlined: (1) when the current mirror carries only DC current and (2) when it carries an AC signal current. For the first scenario, the small signal response is simple, with certain elements of the circuit effectively being open circuits under DC conditions. For the second, the circuit response depends significantly on the input signal, revealing the transfer function relationships.
- MOSFET and BJT Configurations: The section describes how these small signal models differ when employing MOSFETs versus BJTs, with parallel resistances and voltage-dependent current sources being highlighted. The models capture the essential dynamics and potential gain of the circuits.
- Applications: The utility of current mirrors in amplifiers (both common-emitter and common-source types), and how they form part of differential amplifier configurations, is also examined. The significance of matching components in integrated circuits to optimize performance is discussed, underscoring the balance between practicality and theoretical design in real-world applications.
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Introduction to Small Signal Model
Chapter 1 of 6
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Chapter Content
To understand or to appreciate the effect of common current mirror in amplifier standard amplifier where, we normally talk about the linearize circuit whether it is common emitter or common source or common collector or common drain or for that matter even for differential amplifier.
We need to understand the small signal model of current mirror and to go into the small signal model we do have two possible situations. One is the current mirror may not be carrying any signal namely under DC condition what is the small signal equivalent circuit and then we do have the second possible situation where the current mirror may carry signal in the form of current.
Detailed Explanation
The small signal model helps us analyze how circuits respond to small fluctuations in input signals around their operating point. In this specific case, we are looking at the small signal model of a common current mirror used in amplifiers. There are two scenarios to consider: one where the current mirror is only dealing with a DC reference current, and another where it is dealing with a signal current. This distinction is crucial because it influences how we represent the circuit for analysis.
Examples & Analogies
Think of a current mirror circuit as a fountain that usually flows a constant stream of water (DC current). If we want to see how it reacts to waves of water pushed by a pump (signal current), we need to analyze both the situation when there's just the fountain flow and when there are waves. This analysis helps us understand both the steady-state and dynamic responses of the fountain.
Small Signal Model for MOSFET Current Mirror
Chapter 2 of 6
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So, let me talk about the small signal model of current mirror implemented by MOSFET. Here we do have the current mirror circuit, we do have transistor-1 it is diode connected and the we do have reference current DC current that is getting mirrored into this branch through this transistor-2.
For small signal model this is DC current so; obviously, we have to make the current here it is since it is 0. So, we can say it is this circuit is open.
Detailed Explanation
In small signal analysis, we treat DC conditions as constant sources, effectively turning them into 'open circuits' for the purposes of small signal analysis. In a MOSFET current mirror, transistor-1 is often diode-connected, which means it is configured to always conduct. Now, while analyzing the small signal model, we essentially ignore the DC components to focus only on variations introduced by AC signals. This simplification allows us to predict how the circuit behaves when small fluctuations occur.
Examples & Analogies
Imagine you are trying to measure the ripples on the surface of a calm lake (the small signals) while ignoring the sunlight reflecting off the water (the DC current). By covering your eyes from the sunlight, you can better see the ripples, which is analogous to ignoring the DC components in a circuit analysis.
Voltage Conditions in Small Signal Analysis
Chapter 3 of 6
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So, we can say the small signal equivalent circuit whenever we do have a current mirror, then it will be very simple we do have the small signal equivalent circuit of the; small signal equivalent circuit equivalent of application and then we do have simply this resistance r and then of course, in this node it is connected to AC ground.
Detailed Explanation
When we analyze the small signal equivalent circuit of a current mirror, we notice that the output primarily consists of a resistance r, representing how the circuit reacts to small changes in voltage. By grounding the AC components, it allows us to focus on how any small signal coming through is processed by the current mirror without interference from DC levels.
Examples & Analogies
Think of it as tuning into a radio station where the background noise (DC) has been minimized so that you can clearly hear the music (AC signal). You only see how the circuit behaves to those variations, which is how we focus on the small signal aspects.
Small Signal Model for BJT Current Mirror
Chapter 4 of 6
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So, here we do have; here we do have the current mirror and again we do have a reference current is only DC, here we do have the application circuit or application module and we like to draw the small signal equivalent circuit here.
Detailed Explanation
The small signal model for a BJT current mirror is similar to that of a MOSFET, albeit with different parameters due to the inherent characteristics of BJTs. We again treat the DC current as a reference point for analyzing the dynamics of AC signals. In this model, we take into account the internal resistances and configuration of the BJT, allowing us to derive how changes in input current affect output conditions.
Examples & Analogies
Just like listening to how loud the music at a concert gets when the drummer plays harder, we observe the effect of input changes (AC signals) on our output, ignoring the steady hum of the crowd (DC reference current) going on in the background.
Small Signal Model with Signal Current
Chapter 5 of 6
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Situation when may arise when this reference current may have a signal part namely say i . In that case; obviously, this will; this will not be 0 and this may carry some signal to this voltage dependent current source.
Detailed Explanation
When analyzing the small signal model in the presence of an input signal current i, the situation becomes more complex. Here, we must account for both the DC reference and the varying AC signal input. This means we cannot simply ignore the DC level, as it interacts with the fluctuating signal current. The relationship between the signal current and our small signal parameters becomes crucial for understanding how the circuit operates in real time.
Examples & Analogies
Imagine a busy train station where a train is the steady flow of passengers (DC current), and loud announcements about train schedules are the signal currents. When the announcements are made, they impact the overall atmosphere, making it crucial to take them into account, just like the varying input current affects the circuit's behavior.
Application of Current Mirror in Amplifiers
Chapter 6 of 6
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Chapter Content
Now, we have covered this small signal equivalent circuit of current mirror for different cases namely if it if the current mirror is not having any signal current, then it is the equivalent circuit is very straightforward. Whereas, if the current mirror it is having input current then of course, that current it is coming to the application circuit.
Detailed Explanation
After analyzing the small signal equivalent circuits for both scenarios—no signal current versus with signal current—we can see how current mirrors can be used effectively in amplifiers. If the mirror is under steady DC operation, its function is simpler. However, when signal currents are introduced, the analysis reveals how those currents affect overall amplifier performance. This understanding aids in designing circuits that can handle dynamic inputs.
Examples & Analogies
Think of your silverware drawer. When everything is tidy (DC operation), you know where everything is. When you start preparing a meal (introducing signal currents) and take things in and out, you need to rely on your understanding of the drawer's layout to keep things organized and functional, similar to how a current mirror manages different input types.
Key Concepts
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Small Signal Model: A technique for linearizing the behavior of circuits under small input signals.
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DC vs AC Analysis: Differentiating circuit behavior when subjected to direct current versus alternating signals.
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Current Mirroring: The fundamental function of replicating a current from one branch of a circuit to another.
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Applications in Amplifiers: Current mirrors enhance stability and performance in amplifier circuits.
Examples & Applications
In a common emitter amplifier using a BJT current mirror, the mirrored current stabilizes the biasing condition for optimal performance.
A MOSFET current mirror can effectively provide a mirrored output current for a differential amplifier, maintaining balanced operation.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
In a circuit fair, currents run, / Mirrors reflected, jobs are done.
Stories
Imagine a wizard with two identical mirrors; whatever light enters one mirror perfectly reflects in the other—a metaphor for current mirrors sharing current across circuits.
Memory Tools
Remember the acronym 'DCAC' for examining both DC and AC conditions in your small signal models!
Acronyms
**'VCG'** - Voltage Controlled Gain
reminder of the effect these sources have in our analysis.
Flash Cards
Glossary
- Current Mirror
A circuit that forces a specified current to flow in one branch to replicate the current in another branch.
- Small Signal Model
An equivalent circuit that linearizes the behavior of a nonlinear circuit for small input signals.
- DC Conditions
Situations in which alternating currents are not present, allowing for steady-state analysis.
- AC Signal
A time-varying signal that can fluctuate over time, affecting the circuit's behavior.
- MOSFET
A type of field-effect transistor used for switching and amplifying electronic signals.
- BJT
Bipolar Junction Transistor; a type of transistor that uses both electron and hole charge carriers.
Reference links
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