## 2024-06-15

### Transistor Operating Modes

Transistors, specifically Bipolar Junction Transistors (BJTs), operate in four distinct modes: cutoff, active, saturation, and reverse active. To explain these modes in an easy-to-understand way, we can use the "beta man" concept. In this analogy, "beta" represents the current gain of the transistor, or how effectively it amplifies current.

## 1. Cutoff Mode

Beta man is asleep.

In cutoff mode, the transistor is off, and no current flows from the collector to the emitter.

Mathematical Conditions:

• Base-emitter voltage: VBE < 0.7V (for silicon transistors).
• Collector current: IC ≈ 0 because there is minimal base current, IB ≈ 0.

Example:

• Suppose VBE = 0.3V. Since VBE < 0.7V, the transistor remains off.
• If IB = 0.1 μA, then IC ≈ 0, illustrating the lack of significant current flow.

## 2. Active Mode

Beta man is working efficiently.

In active mode, the transistor is on, amplifying the current from the base to the emitter.

Mathematical Conditions:

• Base-emitter voltage: VBE ≈ 0.7V.
• The collector current is given by IC = β IB, where β is the current gain.

Example:

• Let β = 100 (typical for many BJTs).
• Suppose IB = 1 μA. Then, IC = β · IB = 100 · 1 μA = 100 μA.
• Here, VBE ≈ 0.7V, and the transistor is in its active region, amplifying the base current.

## 3. Saturation Mode

Beta man is overworked and struggling.

In saturation mode, the transistor is fully on, and the collector-emitter voltage VCE is low.

Mathematical Conditions:

• VBE ≈ 0.7V.
• Collector-emitter voltage: VCE ≈ 0.2V or lower.

Example:

• Let VBE = 0.7V, and for saturation, VCE ≈ 0.2V.
• With IB = 1 μA and β = 100, IC = β · IB = 100 · 1 μA = 100 μA.
• In saturation, VCE ≈ 0.2V, showing minimal voltage drop across the transistor.

## 4. Reverse Active Mode

Beta man is working in reverse.

In reverse active mode, the transistor behaves differently, typically inefficiently, with the base-emitter junction reverse-biased.

Mathematical Conditions:

• Base-emitter voltage: VBE < 0.
• Collector current is typically much smaller than in the forward active mode.

Example:

• Suppose VBE = -0.7V (reverse bias). The transistor is not designed for efficient operation here.
• With IB = 1 μA, the collector current IC is generally much lower, IC = β' · IB, where β' is much smaller than β.
• If β' = 10, then IC = 10 · 1 μA = 10 μA, which is significantly smaller compared to the forward active mode.

## Summary with Examples:

• Cutoff Mode: VBE < 0.7V, IC ≈ 0.
• Active Mode: VBE ≈ 0.7V, IC = β · IB.
• Example: IB = 1 μA, β = 100 → IC = 100 μA.
• Saturation Mode: VBE ≈ 0.7V, VCE ≈ 0.2V.
• Example: IB = 1 μA, β = 100 → IC = 100 μA.
• Reverse Active Mode: VBE < 0, IC ≈ β' · IB with β' much smaller.
• Example: VBE = -0.7V, IB = 1 μA, β' = 10 → IC = 10 μA.