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.
27.8.1. Changes in Input and Output Resistance
Learn content
Interactive Audio Lesson
Unlock the classroom podcast
The transcript is free to read. A free account plays the conversation back.
Today we'll discuss how we derive the formula for output voltage and gain in a common emitter amplifier. The output voltage can be expressed as v_out = -g_m * R_C * v_be. Can anyone tell me what each of these terms represents?
g_m is the transconductance and R_C is the collector resistance.
Exactly! The negative sign indicates phase inversion. Now, we need to find the relationship between input and output voltage further. What do you think happens to the output voltage if R_E is significant?
I think it might reduce the gain since more voltage drops across R_E.
Correct! The formula shows that as we increase R_E, the output voltage decreases, hence the gain A becomes A = -(g_m * R_C) / (1 + g_m * R_E). Let's remember this: R_E stabilizes the circuit but at a cost to gain! A good mnemonic is 'Gain gets Gain-ted down.'
That's a funny saying!
Indeed! Let’s recap: Larger R_E stabilizes but reduces gain. Are we clear?
Yes, I understand!
Unlock the classroom podcast
The transcript is free to read. A free account plays the conversation back.
Now, let’s calculate the input resistance, R_in. Who remembers how to approach this derivation?
We start by applying a test voltage and measuring the current.
Right! If we apply a voltage v_x and measure the base current i_x, the input resistance is defined as R_in = v_x / i_x. Based on our circuit, we can write this as R_in = r_pi + (1 + β) * R_E. What's the significance of the 1 + β term?
It accounts for the amplification factor because the base current is amplified in the collector current.
Exactly! Remember: larger β means larger input resistance. Also, don't forget, R_in primarily governs how the amplifier interacts with the preceding stage.
So a low input resistance allows more current to flow into the base?
Correct! Always strive for optimal R_BB to balance the input resistance with the attached load.
This makes sense!
Unlock the classroom podcast
The transcript is free to read. A free account plays the conversation back.
Let’s move on to the output resistance, R_out. How can we determine this?
Isn’t it similar to calculating input resistance, applying a test voltage?
Correct! We apply v_y at the output port while grounding the input and measure the output current i_y. The output resistance is given by R_out = v_y / i_y. But what’s interesting about the current source?
The current source effectively isolates the output resistance in parallel.
Exactly! In practice, we find R_out simplifies to just R_C with a significant role of any added resistances on the output side. Always picture the current source as providing infinite resistance. What’s the key takeaway here?
R_out is largely determined by R_C, which doesn't allow for significant variations.
Exactly! Don’t forget, R_out influences how effectively the amplifier can drive a load. Healthy understanding here helps in design decisions. Let’s summarize: R_out is mainly R_C, focusing on how it connects with the load.
Unlock the classroom podcast
The transcript is free to read. A free account plays the conversation back.
Now we need to tie everything together with the impact of R_E on overall circuit stability. Why do we use emitter resistors?
To stabilize the operating point against changes in β.
Very good! The downside is that it also affects our voltage gain. Does anyone recall our earlier gain equation including R_E?
Yes! The gain gets reduced based on the value of R_E.
Spot on! That's why we need to size R_E carefully—it's a balancing act! We want stability without sacrificing much gain. Can someone remember a practical design rule for selecting R_E?
Keep it small relative to the (1+β) times R_E?
Yes, excellent! Adhering to this helps maintain stable performance—and thus a reliable amplifier.
Overview
Short Summary
This section discusses the significance of input and output resistance in common emitter amplifiers and their impact on voltage gain.
Medium Summary
The section delves into how input and output resistance in a common emitter amplifier relate to its overall performance, including the effects of emitter resistance on voltage gain and the implications for circuit stability. It also covers the mathematical expressions for these resistances, emphasizing their roles in amplifier design.
Detailed Summary
Changes in Input and Output Resistance
In this section of the lecture, we explore the small signal equivalent circuit of the common emitter amplifier, focusing on how input and output resistances affect the amplifier's performance. The formulas for voltage gain, input resistance, and output resistance are derived step by step, demonstrating the influence of emitter resistance (R_E) on the circuit characteristics.
The output voltage can be expressed in terms of the transconductance (g_m) and the collector resistance (R_C). Upon simplifying the original formula, we establish that the voltage gain A is affected negatively by the emitter resistance, which stabilizes the operating point against variations in beta (β) but also reduces gain.
The input resistance (R_in) of the amplifier is determined by the parallel connection of the base resistance and the effective resistance of the circuit, including emitter resistance multiplied by (1 + β). The output resistance (R_out) is analyzed similarly, incorporating the characteristics of the current source and the emitter resistor.
The significance of appropriately sizing R_E is also discussed, balancing the need for circuit stability with the requirement for adequate voltage gain. The section concludes with an overview of how to reinstate voltage gain by strategically utilizing capacitors to ground the emitter during AC conditions while preserving the DC operation.
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 accountApart from the voltage gain open loop voltage gain, we do have two more important parameters namely input resistance and output resistance of the model.
Detailed Explanation
In this section, we introduce two critical parameters of the amplifier model: input resistance and output resistance. Understanding these parameters is essential because they significantly influence how the amplifier interacts with the rest of the circuit. Input resistance determines how much of the input signal is accepted, while output resistance affects how the amplifier delivers the output signal to the load. Therefore, both values are vital for optimizing amplifier performance and ensuring it functions effectively within a circuit.
Examples & Analogies
Think of input resistance as the width of a doorway through which people (signals) need to pass. A wider doorway (higher input resistance) allows more people through with less effort, while a narrower doorway (lower input resistance) could create a bottleneck, slowing down the flow. Similarly, output resistance is like how well a water hose pushes water out. If the hose is too narrow (high output resistance), less water can get through, just like a signal output getting impeded.
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, let us find the expression of this input resistance of this circuit. So, I do have another slide for that, yes. This is the main circuit and whenever we are going to find a small signal parameter....
Detailed Explanation
To find the input resistance, we observe the circuit's response to a known input signal. We measure the voltage drop across the components and the current flowing through them to calculate the resistance using Ohm's law (Resistance = Voltage / Current). In this particular setup, resistive elements and transistor characteristics combine to define the input resistance of the amplifier.
Examples & Analogies
Imagine you’re measuring the resistance of a garden hose. You send water (the input signal) through the hose and measure how much water gets through (current) while also checking the pressure drop (voltage). The easier the water flows through, the lower the resistance of the hose. In electronics, the same principle applies when measuring how freely a signal can pass through the circuit.
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, let me analyze the output port and let me see that what is the corresponding expression of the output resistance....
Detailed Explanation
Similar to input resistance, output resistance is calculated by applying a signal at the output and measuring the resulting current. The output resistance influences how well the amplifier can drive the load. Generally, the output resistance is lower to ensure that the signal can drive external circuits effectively without significant loss.
Examples & Analogies
Think of output resistance as the strength of a person pushing against a closed door. If they're weak (high output resistance), they'll struggle to push it open (send the signal out). But if they’re strong (low output resistance), they can easily blow open the door and continue into the next room (load), ensuring your signal reaches its destination without much attenuation.
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, the a purpose more main motivation of putting this R, it is to stabilize the operating point of the circuit in case if beta is changing....
Detailed Explanation
The emitter resistor, designated as R_E, is essential for stabilizing the amplifier's operating point against variations in the transistor's beta parameter. While it helps ensure consistent operation, it can also reduce gain, which means its value must be considered carefully in the design process. More resistance in the emitter leg leads to lower gain, which is a trade-off designers must balance.
Examples & Analogies
Consider an athlete using weights to maintain their performance while running. The weights enhance stability and control initially but slow them down. Similarly, while the emitter resistor improves the stability of the amplifier, it can inadvertently reduce the signal gain, making it crucial to find a balance that maintains performance without compromising too much on gain.
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 accountWe can say that this is R' and then total input resistance of the voltage amplifier....
Detailed Explanation
When analyzing impedance, it's important to consider all resistances present in the circuit. The input resistance is calculated by combining the effects of inherent resistive components and external input resistors. By mapping these resistances and understanding their interactions, one can ensure that the amplifier is designed effectively to interface smoothly with other circuit components.
Examples & Analogies
Think about setting up a water system with pipes of different sizes. If one pipe is too wide and another too narrow, it can cause issues in water flow and pressure. Similarly, when designing circuits, accommodating the various resistances properly ensures that signals move through the circuit without causing bottlenecks or interference.
--
Key concepts
Core takeaways and short definitions to help you quickly recall the key ideas from this section.
- Output Voltage (v_out):
The voltage produced by the common emitter amplifier, shown to depend on g_m and R_C.
- Voltage Gain (A):
Ratio of output voltage to input voltage; decreases with high R_E.
- Input Resistance (R_in):
Determined by the base resistance and (1 + β) factor; crucial for stability.
- Output Resistance (R_out):
Primarily influenced by R_C, it affects load driving capabilities.
- Emitter Resistance (R_E):
Stabilizes transistor operation but can limit gain if too significant.
Examples
Step-by-step examples to apply the section's ideas and test your understanding.
If you have a common emitter amplifier with g_m = 10 mA/V and R_C = 1 kΩ, the maximum output voltage can be calculated using the formula and may yield significant amplification depending on R_E.
Consider a transistor amp with β = 100 and an R_E of 100Ω which drastically reduces the voltage gain by a factor of (1 + 100).
Memory aids
Imagine a tightrope walker (the amplifier) balancing (gain) under a windy nature (R_E) that causes fluctuations; to stabilize, they use weights (R_E), which makes them move slower (reduced gain).
Remember GAIN: G for gain, A for amplitude, I for input, N for node; these all influence how a circuit works.
Flash Cards
Glossary
g_m
Transconductance, a measure of how effectively a transistor converts input voltage to output current.
R_C
Collector resistance, affecting output voltage and gain.
R_E
Emitter resistance, used for biasing to stabilize operating point but can reduce gain.
β (Beta)
Current gain of the transistor, crucial for determining current amplification.
R_in
Input resistance of the circuit, affecting how much input signal can be applied.
R_out
Output resistance, representing the impedance the amplifier presents to the load.