a. Based on a review of the characteristics of Fig. 124, which parameter changed the least for t

A. Based on a review of the characteristics of Fig. 124,...

Key Concepts

Transistor h?Parameter Model

This concept refers to the set of parameters (typically h_ie, h_re, h_fe, and h_oe) used to model the small-signal behavior of a transistor. These parameters describe how the transistor responds to small variations in its input and affect properties such as input impedance, reverse voltage gain, current gain, and output admittance. They are essential for analyzing and designing circuits where linear approximations of transistor behavior are valid.

Parameter Variation with Operating Point

This concept involves understanding how the various h-parameters change with the operating conditions, particularly the collector current. It is crucial to identify which parameters remain relatively stable and which vary significantly across the operating range. This analysis helps in determining the reliability of approximations and the performance of the transistor in different regions of operation.

Output Admittance and Impedance

The parameter h_oe represents the transistor’s output admittance, and its reciprocal (1/h_oe) is indicative of the output impedance. This concept is important because in circuit analysis, predicting how the transistor interacts with an external load resistor can depend critically on whether the load dominates or if the transistor’s intrinsic output impedance plays a significant role. Understanding the range and behavior of 1/h_oe is key to applying appropriate approximations in design.

Approximation Validity in Circuit Analysis

Approximations such as treating a parallel combination of the load resistor and the transistor's output impedance as simply the load resistor, or approximating the product h_re·V_ce as negligible, are based on assumptions about the relative magnitude of circuit parameters. This concept covers identifying the conditions under which such simplifications are valid, notably at specific levels of collector current or within certain operating regions, which in turn simplifies analysis and design.

Transistor Operating Regions

Transistors operate in different regions such as cutoff, active, and saturation, each exhibiting distinct behavior in terms of amplification and impedance characteristics. Recognizing the operating region is essential when applying approximations, as the reliability of simplified models (for example, neglecting the reverse voltage gain times V_ce) can vary significantly depending on whether the transistor is, for instance, operating at low or high collector currents.

Transcript

00:02 So for the first part we have to find r and let's first write down the information that we already have.

00:17 So we have power and we have the emf also.

00:25 And let's try to connect these three equations.

00:30 So we know that power is equal to square of the voltage over equivalent.

00:37 Resistance.

00:38 So let's write down the equivalent resistance hoping that we will get this expression equivalent resistance in terms of r.

00:49 So the equivalent resistance will be 7 ooms.

00:55 So this is the resistor that is in series with a parallel combination of resistors 12 oom, 4 oom and r.

01:09 So this that i'm writing is just the equivalent resistance of the parallel combination of these three resistors.

01:26 Now we can substitute this expression over here.

01:31 Like i would suggest you not to worry about this oom sign and just remove this and solve the rest of the equation because this is this sign is really bother.

01:48 This sign really bothers me while solving this equation.

01:52 So yeah, don't worry about this unit.

01:55 You can plug it later.

01:59 So now you can substitute these two values over here.

02:04 So our equivalent will be equal to square of the emf over power and this will be equal to this whole expression.

02:17 Now substituting all the values along with the voltage and power and solving for r you should get r to be equal to 19 .5 ooms now this equation is really easy to solve it will be a linear equation not a quadratic one or a polynomial equation so yes this equation is going to be really easy you just have to cross multiply all the terms and solve all r so now for the second part we have to find r so we know that from this equation we see that power is proportional to r equivalent so here i'm using power to be equal to square of the current times equivalent resistance so by from this equation you have power to be proportional to equivalent resistance and we therefore in order to minimize power okay so oops okay so actually we are using the same equation so this is the equation that we are going to follow again so according to this equation our emf is constant which means that power is inversely proportional to the equivalent resistance which means that the maximum power will occur at the minimum resistance.

04:19 So let me just write this.

04:21 So p max will occur at the minimum equivalent resistance.

04:29 And for the minimum equivalent resistance, so let's take a look at this equation.

04:35 Now this is possible when r is equal to 0, that way the minimum, the equivalent resistance will just be 7 oombs.

04:46 So for that, we need r to be equal to 0 for maximum power and obviously minimum equivalent resistance...

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