Repeat problem 11.42 (a) with RC=1 k Ω(b) with RC=2 k Ω |...

Name: Problem 47, Chapter 11: Essentials of Electrical and Computer Engineering
Uploaded: 2021-07-05T21:18:39-08:00
Duration: 7 min 3 s
Channel: Meghan Miholics
Description: Repeat problem 11.42 (a) with RC=1 k Ω(b) with RC=2 k Ω

Key Concepts

Effect of Component Variation

Studying how changes in components such as the collector resistor affect circuit performance is fundamental in circuit design. By analyzing different values (for instance, RC = 1 k? versus RC = 2 k?), one can understand the sensitivity of the amplifier's bias point, gain, and overall stability, thereby allowing for optimization of performance parameters.

Common-Emitter Amplifier

This is a fundamental transistor configuration in analog electronics where the emitter terminal is common to both the input and output circuits. It is widely used because it provides significant voltage gain and phase inversion, making it ideal for signal amplification and processing.

Collector Resistor (RC)

The collector resistor plays a critical role in determining the operating point and amplification level of a transistor circuit. By setting the voltage drop across the collector, RC helps in establishing the quiescent collector current and, consequently, affects the voltage gain and linearity of the amplifier.

DC Biasing

DC biasing involves establishing the correct DC operating point of a transistor to ensure it operates in the desired region, typically the active region for amplification. Proper biasing guarantees that the transistor remains stable throughout signal variations and minimizes distortion in the output.

Small-Signal Analysis

This technique is used to analyze the behavior of nonlinear circuits, like those involving transistors, by linearizing them around their DC operating point. It allows engineers to predict the AC voltage gain, input and output impedances, and other frequency-dependent characteristics of the amplifier, which are crucial for signal processing applications.

Transcript

00:01 In this question, we are asked to consider the rc circuit shown in figure 2144, and to find a, the time constant, b, the initial current for the circuit, and c, if we are to increase or decrease the resistance of the 6 .5 -on resistor in order to increase the time constant of the overall circuit.

00:27 So starting with part a, we've asked to find the time constant.

00:32 Tau, which corresponds to r times c.

00:37 Now, all of the formulas that we have for rc circuits, technically are just containing one resistor and one capacitor.

00:46 So the first thing that we need to do with this circuit, since it does contain three resistors, is basically just take those three resistors and calculate an equivalent resistance so that they effectively just become one big resistor.

00:59 So the part of the circuit, i will just redraw a part of the circuit that has the resistors.

01:07 That looks like this.

01:12 Whoops.

01:16 Let's do that a bit nicer.

01:17 There we go.

01:19 Okay, and that's going out to the rest of the circuit like this.

01:22 So this is 24 oms.

01:24 This is 6 .5 oms.

01:27 And then this is 13 oms.

01:31 So to do an equivalent resistor, resistance, we're first going to take these two, which are in series with one another, and add them together.

01:42 So the equivalent resistance for those two in series is going to be 13 plus 6 .5, so that goes 19 .5 oms.

01:55 And then we just have basically a 19 .5 oom resistor in parallel with a 24 -oom resistor.

02:03 So we're going to do an equivalent resistance for that, in which we have to use the reciprocal values and add them together.

02:15 Okay, so we're going to do one divided by 24, one divided by 19 .5, add those together, and then just do one over that to get the equivalent resistance.

02:29 So that's going to be 10 .75, 10 .76, let's say, alms.

02:38 Okay, so now that we have that equivalent resistance, we can go ahead and calculate our time constant.

02:42 So that's going to be 10 .76 oms times the capacitance, which was given as 62 micro -ferds that you can just read from the circuit diagram.

03:00 Okay, so that's going to be 667.

03:08 Since we kept the capacitor, capacitance in micro, that's going to make our time constant in microseconds.

03:17 Okay, or we could convert that into seconds or milliseconds...

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