Poisson Distribution

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Questions and Answers

In an NPN transistor, if the emitter-base junction is forward-biased, what constitutes the emitter current (Ä°E)?

  • Equal parts electrons injected from the emitter into the base and holes from base to emitter
  • Primarily electrons injected from the emitter into the base. (correct)
  • Primarily holes injected from the base into the emitter.
  • Only minority carriers from the base to the emitter.

For a PNP transistor, what primarily constitutes the emitter current (IE) when the emitter-base junction is forward-biased?

  • Primarily electrons injected from the emitter into the base.
  • Primarily holes injected from the emitter into the base. (correct)
  • Only minority carriers moving from base to the emitter.
  • Equal parts electrons injected from the emitter into the base and holes from base to emitter.

Why is the conductivity of the emitter region made significantly higher than that of the base in a BJT?

  • To ensure the current is primarily due to majority carriers from the emitter. (correct)
  • To reduce the overall current flow through the transistor.
  • To ensure that the current is mainly due to minority carriers.
  • To achieve equal concentration of both majority and minority carriers.

In an NPN transistor, what happens to the electrons injected into the base from the emitter?

<p>Most reach the collector junction, contributing to collector currrent. (D)</p> Signup and view all the answers

If $I_E$, $I_C$, and $I_B$ represent the emitter, collector, and base currents respectively in a transistor, which equation accurately describes their relationship?

<p>$I_E = I_C + I_B$ (B)</p> Signup and view all the answers

What is the leakage current ($I_{CO}$) in a transistor?

<p>The collector current when the emitter is open. (D)</p> Signup and view all the answers

What does the DC current gain ($\alpha_{dc}$) represent in a transistor?

<p>The fraction of emitter current that reaches the collector. (D)</p> Signup and view all the answers

Why is the value of $\alpha_{dc}$ typically less than 1?

<p>Because some carriers recombine in the base region. (B)</p> Signup and view all the answers

What is the typical range of values for $\alpha_{dc}$?

<p>0.95 to 0.99 (B)</p> Signup and view all the answers

What does the AC current gain ($\alpha_{ac}$) represent?

<p>The ratio of change in collector current to change in emitter current. (C)</p> Signup and view all the answers

How does the value of $\alpha_{ac}$ typically compare to that of $\alpha_{dc}$?

<p>$\alpha_{ac}$ is approximately equal to $\alpha_{dc}$. (B)</p> Signup and view all the answers

According to the sign conventions for transistor currents, which direction is considered positive for current entering a terminal?

<p>Entering the terminal. (C)</p> Signup and view all the answers

Within the sign conventions for transistor voltages, when is a voltage considered positive?

<p>When the first subscript is positive relative to the second. (C)</p> Signup and view all the answers

If $V_{EB}$ is positive, what does this indicate?

<p>The emitter is positive with respect to the base. (A)</p> Signup and view all the answers

A transistor is considered a how many terminal device?

<p>Three-terminal device (A)</p> Signup and view all the answers

What is a common practice when using a transistor as a two-port device?

<p>Grounding one of the terminals. (D)</p> Signup and view all the answers

What are the three terminals of a BJT?

<p>Emitter, base, collector (A)</p> Signup and view all the answers

In circuit diagrams employing NPN and PNP transistors, what dictates the direction of current flow?

<p>Polarity of the transistor and biasing (A)</p> Signup and view all the answers

Given a BJT circuit, how does one typically analyze it initially?

<p>As a three-terminal device with defined input and output ports. (A)</p> Signup and view all the answers

Flashcards

IE= IC + IB

The sum of collector current (Ic) and base current (IB) equals emitter current (IE).

Ico

Collector current resulting from minority carriers.

αdc (DC current gain)

Ratio of collector current (Ic) to emitter current (IE) in DC conditions. Typically less than 1.

αac (AC current gain)

Ratio of change in collector current (ΔIc) to change in emitter current (ΔIE). Similar to αdc but in dynamic (AC) conditions.

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Sign Conventions

In circuits, current entering a terminal is positive, and current leaving is negative. Voltage is positive if the terminal is positive relative to ground.

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Three Terminal Device

A transistor with three terminals: Emitter, Base, and Collector.

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Study Notes

  • The Poisson distribution models the probability of a number of events occurring in a fixed interval, given a constant mean rate and independence from the last event.

Common Applications

  • Modeling telephone calls to a call center per hour
  • Modeling cars passing a point on a highway per minute
  • Modeling customers entering a store per day
  • Modeling defects in a manufactured product per unit
  • Modeling meteorites greater than 1 meter diameter striking Earth per year
  • Modeling goals scored in a soccer game

Probability Mass Function

  • The probability of observing x events in a given interval: $P(X=x) = \frac{e^{-\lambda}\lambda^x}{x!}$
    • Where x is the number of events
    • $\lambda$ is the average number of events per interval
    • e is Euler's number (approximately 2.71828)

Example Call center

  • A call center receives 10 calls per hour on average.
  • The probability of receiving exactly 5 calls in the next hour is calculated using the Poisson distribution:
    • $P(X=5) = \frac{e^{-10}10^5}{5!} = 0.0378$
    • There's a 3.78% chance of receiving exactly 5 calls.

Assumptions

The Poisson distribution relies on these assumptions:

  • Events occur randomly and independently.
  • The average rate of events $(\lambda)$ is constant.
  • Probability of an event in a small interval is proportional to the interval's size.
  • The probability of multiple events in a small interval is negligible.

Properties

  • The mean of the Poisson distribution is $\lambda$
  • The variance of the Poisson distribution is $\lambda$
  • The standard deviation of the Poisson distribution is $\sqrt{\lambda}$

Example Factory

  • A factory produces light bulbs with a 0.01 probability of being defective
  • In a random sample of 100 light bulbs, we can use the Poisson distribution to approximate the probability of finding exactly 2 defective bulbs:
    • $\lambda = np = 100 * 0.01 = 1$
    • $P(X=2) = \frac{e^{-1}1^2}{2!} = 0.1839$
    • There is approximately 18.39% chance of finding exactly 2 defective light bulbs in the sample

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