Electrical Energy Technology

Electrical Energy Technology

Electrical Energy Technology

Modern Transistor Theory Guide

Contents

1. Voltage and Current References

1.1 PNP Transistor

For the typical flow direction in a PNP transistor:

\[ I_B < 0 \text{ and } I_C < 0, \text{ while } I_E > 0 \] \[ \text{Furthermore } V_{BE} < 0 \]

1.2 NPN Transistor

For the typical flow direction in an NPN transistor:

\[ I_B > 0 \text{ and } I_C > 0, \text{ while } I_E < 0 \] \[ \text{Furthermore } V_{BE} > 0 \]

2. The IV Input Characteristic of a Transistor

The IV input characteristic of a Si-NPN transistor looks exactly as the IV characteristic of a Si-diode. This is not surprising, because the base-emitter is a PN junction and it is also a PN junction we have in a diode from the Anode to the Cathode.

For the diode and for the transistor the IV characteristic shows the current through the PN junction as a function of the voltage across the PN junction. In the transistor input characteristic, the current through the PN junction is considered to be the current IB into the base which continues through the PN junction to the emitter.

Key Points:

  • Base current threshold ≈ 20 µA for conducting state
  • Operating region begins at VBE ≈ 0.5V
  • Sharp current increase above threshold

3. The IV Output Characteristics of a Transistor

Figure 62.3.1 shows an example of IV output characteristics of a transistor. What makes this figure particularly interesting is that it actually shows many IV output characteristics in the same graph. For each specific value of the base current IB, we have a different output characteristic.

Let's examine what happens with IB = 20 µA:

  1. We start at point (0,0)
  2. As VCE increases slowly, the collector current IC increases quickly along the very steep red line
  3. This continues until IC reaches 2 mA
  4. After this point, IC becomes constant and follows the dark purple horizontal line to the right as VCE increases further

Similarly, if we look at the case where IB = 40 µA, we see the same pattern but with different values: The collector current rises quickly until it reaches 4 mA, then remains constant as VCE continues to increase.

Key Behavior:

  • When IB = 0, then IC = 0
  • When we turn on IB to a specific value (like 40 µA), we can have current flow in the main direction
  • This current can be much larger than IB (typically 100 times larger)

The transistor essentially behaves like a current-controlled switch. It can turn on and off a current in the main flow direction that is much larger than the control current IB. This is where the amplification property of transistors comes from.

Current Gain (β):

\[ \beta = \frac{I_C}{I_B} \]

Also sometimes denoted as hFE, the current gain β varies by transistor type:

  • Power transistors: β ≈ 10
  • General-purpose transistors: β ≈ 100
  • Small signal transistors can reach β ≈ 1000

4. The Three States of a Transistor

Figure 62.4.1 shows an IV output characteristic of a transistor together with an indication of the three different states. Understanding these states is crucial for proper transistor operation.

4.1 The Cutoff State

The cutoff state represents the "OFF" condition of the transistor. In this state:

\[ V_{BE} < V_{BE(on)} \Rightarrow I_B = 0 \Rightarrow I_C = 0 \]

When VBE is smaller than VBE(on) (the base-emitter voltage needed to activate the PN junction), the "BE diode" is off. This means IB = 0, which consequently leads to IC = 0.

4.2 The Saturation State

The saturation state represents the "fully ON" condition. Here's what happens:

\[ V_{BE} = V_{BE(on)} \Rightarrow I_B > 0 \Rightarrow I_C > 0 \]

When VBE equals VBE(on), the "BE diode" turns on, allowing current flow. For example, with IB = 60 µA and β = 100:

\[ \beta I_B = 100 \cdot 60 \text{ μA} = 6 \text{ mA} \]

In the saturated state:

\[ 0 < I_C < \beta I_B \]

4.3 The Active State

The active state is where the transistor operates as an amplifier. Following our previous example with IB = 60 µA:

\[ V_{BE} = V_{BE(on)} \Rightarrow 0 < I_B , I_C = \beta I_B , R_{Sat} I_C < V_{CE} \]

In this state, IC remains constant at β·IB while VCE can vary. This is the region where the transistor is most commonly used for amplification.

5. The Transistor Circuit with a Collector Resistance

The Load Line

\[ I_C = \frac{V_{CC} - V_{CE}}{R_C} = -\frac{1}{R_C}V_{CE} + \frac{V_{CC}}{R_C} \] Key points: \[ V_{CE} = 0 \Rightarrow I_C = \frac{V_{CC}}{R_C} \] \[ I_C = 0 \Rightarrow V_{CE} = V_{CC} \]

6. Depiction of IC versus IB

In the active region: \[ I_C = \beta I_B \] At saturation point S: \[ I_{C,S} = \frac{V_{CC}}{R_{Sat} + R_C} \] \[ I_{B,S} = \frac{I_C}{\beta} \]

7. Depiction of VCE versus IB

\[ V_{CE} = V_{CC} - R_C\beta I_B \] At saturation: \[ V_{CE,S} = V_{CC} - R_C\beta I_{B,S} \]

For IB = 0 we have VCE = VCC. For increasing IB through the active region, we have an increasing IC = βIB and following a decreasing potential at the collector. At point S, the collector current IC cannot grow further and remains constant at higher IB values.

Important Design Considerations:

  • Maximum operating voltage: \(V_{CE(max)}\)
  • Maximum collector current: \(I_{C(max)}\)
  • Power dissipation: \(P_{max}\)
  • Temperature coefficient: \(\Delta V_{BE}/\Delta T\)

Electrical Energy Technology

Electrical Energy Technology