86.5.2 - Effect of Beta on Current
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Introduction to Current Mirrors
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Welcome, students! Today we're discussing current mirrors, which are essential in analog circuits for setting reference currents. Can anyone explain what a current mirror does?
A current mirror replicates a current through another device, maintaining a constant current in circuits.
Exactly! It allows us to create a precise situation where the output current is based on a set reference value. Now, who can tell me how we might measure the effectiveness of a current mirror?
We can evaluate its output current and stability with varying conditions.
Great point! One significant factor influencing output current is the transistor's beta (β). Let’s remember: High β means better current gain, aiding in accurate current replication. What do you think happens if β is low?
The current mirrors may not copy the reference current well, leading to inaccuracies.
Correct! Inaccuracies arise as base currents start drawing more, affecting the overall mirror's performance.
MOSFET vs BJT Current Mirrors
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Now, let’s compare the current mirrors built using MOSFETs and BJTs. Can someone mention a significant difference?
MOSFETs usually have a higher input impedance compared to BJTs.
Exactly! That's a key point. MOSFET input configurations are generally easier to manage as well. Let’s think about how this affects output current as we analyze different circuits. What factors might we need to account for in BJTs specifically?
We'll need to consider the Early voltage since it can introduce non-ideality.
Precisely! Early voltage will affect the performance as it impacts output resistance. Understanding these nuances is critical in achieving high precision in current mirrors.
Numerical Example Calculations
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Let’s take a numerical example to calculate the output current. If we have a 0.5 mA reference current in a circuit with given K factors, how would we start?
We would use the formula I_DS2 = I_REF * (K2 / K1).
Good start! Now, assuming K1 is 1 mA/V^2 and K2 is 4 mA/V^2, what would I_DS2 be?
Using the formula, I_DS2 = 0.5 mA * (4 mA/V^2 / 1 mA/V^2) would give us 2 mA.
Excellent! You just replicated the output current successfully. Note that this process helps us to design stable current sources in various applications.
Effects of Base Current in BJTs
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Now, let’s discuss how base current affects BJTs in current mirrors. What do you think the effect of base current on overall output current is?
I think it could lower the output current because some of the current is taken up by the base.
Right! This effect is amplified in configurations with multiple BJTs. What can we do to mitigate this problem?
We could use a Beta-helper circuit to minimize base current loss.
Excellent! A Beta-helper circuit effectively boosts the current gain, helping to maintain accurate output even for lower β transistors.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
In this section, we explore the effect of transistor beta (β) on current, focusing on BJT and MOSFET current mirrors. We examine numerical examples detailing current mirror configurations, their applications, and calculations involving reference currents and output biases.
Detailed
In Section 5.2, titled 'Effect of Beta on Current', we delve into the influence of the transistor beta (β) on the output current in current mirror circuits. The section elaborates on the construction of current mirrors using both BJTs and MOSFETs, emphasizing various numerical examples that demonstrate the practical application of these concepts. The discussions include the calculation of output currents given a reference current and how to consider non-ideality factors, such as base current losses (β effect) and Early voltage adjustments. This section underlines the significance of understanding these parameters to design precise current mirrors in analog circuits. The teacher provides step-by-step calculations for different scenarios, highlighting the dependencies of output current on β and illustrating real-world applications of current mirrors.
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Understanding Beta in BJTs
Chapter 1 of 3
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Chapter Content
In this example we do have Q1 and Q2. Now it is forming the current mirror and in this case, just for a change, instead of giving a reference current, we are giving a resistor here, supply voltage it is given to us 12 V. This R resistor in resistance it is 22.8 kΩ and then we can assume that V_BE for both the transistors are approximately 0.6 V. In addition to that, we also have the information about reverse saturation current of the 2 transistors. So, Q1 is having reverse saturation current of 9.5 × 10‒14 A. On the other hand, for Q2 we do have reverse saturation current which is 2.85 × 10‒13 A.
Detailed Explanation
In this chunk, we look at how two bipolar junction transistors (BJTs), labeled Q1 and Q2, are used to create a current mirror circuit. We start with the assumption that both BJTs have a base-emitter voltage (V_BE) of about 0.6 volts, which is a typical value for silicon BJTs. The supply voltage is 12 volts, and a resistor adjusting the circuit current is 22.8 kΩ. Additionally, we consider the reverse saturation currents for both transistors, which indicate how they behave under specific conditions. Q1 has a much lower reverse saturation current compared to Q2, which has implications on their performance in the circuit.
Examples & Analogies
Consider a team of two athletes, each with their own strengths and weaknesses. Q1 is like a sprinter with a naturally low stamina, suitable for short bursts but less effective in longer competitions. On the other hand, Q2 is like a marathon runner, who handles long distances but may not be as quick for short sprints. Together, they collaborate in a relay race—each playing their specific role based on their strengths.
Beta and Non-Ideality Factors
Chapter 2 of 3
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Chapter Content
To get the reference current I_REF, we perform the calculation with I = (I_REF) / 3 = 0.5 mA. If we consider a situation where both the β's are very high, early voltages are also very high, meaning the non-ideality factor is approximately 1.
Detailed Explanation
This segment explains how to find the reference current (I_REF) in the current mirror circuit. The relationship between the output current and the reference current is expressed as I = (I_REF) / 3. When both the gain factors (beta, β) for the BJTs are assumed to be high, along with very high early voltages, we simplify the non-ideality factor to approximately equal 1. This indicates that the circuit operates ideally, without significant losses or deviations.
Examples & Analogies
Think of this concept like a perfectly tuned orchestra. If all musicians (transistors) are playing harmoniously (high beta), the music produced (output current) closely resembles the composer’s original piece (ideal behavior). When the musicians occasionally miss a note or fall out of sync (non-ideality), the music becomes less recognizable, but if their skills and tuning are close to perfect, the performance is impressive.
Impact of Finite Beta on Current Output
Chapter 3 of 3
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Chapter Content
Now, if I consider finite β, the non-ideality factor becomes significant, and using this non-ideality factor we can multiply the output current to find a more realistic value.
Detailed Explanation
Here, we discuss the influence of finite beta (β) on the output current of the BJT current mirror. When the beta values are not infinitely high, the non-ideality factor starts to matter. This means that instead of assuming all current flows ideally, we must calculate how much current is lost through factors like beta. By applying the non-ideality factor to the current output equation, we arrive at a more realistic current output that reflects how the circuit operates in practice.
Examples & Analogies
Imagine feeding two pipes connected to a water tower to nourish a garden. The first pipe (ideal, high beta) allows water to flow freely, while the second pipe (finite beta) has some curves and kinks that reduce the flow. As a gardener, if you observe less water reaching the plants than expected, you realize the second pipe isn’t functioning at full capacity, affecting your irrigation overall. The finite beta in the circuit similarly affects the 'flow' of current.
Key Concepts
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Current Mirror: A circuit that replicates a reference current in different nodes.
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Effect of Beta: The impact of transistor current gain on the output current of current mirrors.
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Early Voltage: A factor that represents non-ideal behaviors in BJTs affecting their output.
Examples & Applications
Given a reference current of 0.5 mA and K factors of a BJT current mirror of K1=1 mA/V^2 and K2=4 mA/V^2, the output current I_DS2 can be calculated.
A BJT current mirror with reverse saturation currents of 0.5 mA and a beta of 150 will exhibit variations of I_DS based on these parameters.
Memory Aids
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Rhymes
When beta's high, the flow won't die, mirrors are strong, and currents belong.
Stories
Picture a mirror in a room that perfectly reflects not just light but also currents, keeping everything in sync and stable.
Memory Tools
MEMORY - M for Mirror, E for Effect of Beta, M for MOSFETs, O for Output Current, R for Reverse Saturation.
Acronyms
C.M.A.B. - Current Mirror, Amplifier, Beta, Accuracy.
Flash Cards
Glossary
- Current Mirror
A circuit that mirrors a reference current to provide a controlled output current.
- Beta (β)
A parameter that represents the current gain of a BJT.
- Early Voltage
A measure of the output voltage dependency in BJTs regarding the collector current.
- K Factor
A parameter that represents the transconductance of a MOSFET.
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