current sources

current sources

1. What a Current Source Is

Current source maintains a specified current $I_s$ through its terminals independent of voltage across (ideal). $V$ determined by external circuit: $V = I_s·R_{load}$ for resistive load.

• Ideal current source: $I = I_s$ constant for any $V$ (internal parallel resistance $R_p =∞$). $I$–$V$ is vertical line.
• Practical current source: $I = I_s - V/R_p$ with parallel internal resistance $R_p$ (large, e.g., $100$ kΩ). Current drops slightly with voltage (leakage).

2. Independent vs Dependent

• Independent: $I_s$ fixed (ideal current source, lab current supply).
• Dependent: $I_s = k·V_x$ or $k·I_x$ (voltage-controlled current source VCCS etc., used in transistor models: $I_C = β I_B$).

3. Symbols and Combinations

Ideal current source: circle with arrow indicating current direction
Series/parallel: ideal current sources of different values cannot be series (conflict → infinite voltage); in parallel: I_eq = Σ ± I_si (sign by direction)
Practical with Rp can be combined.

• Series: same current must flow; different $I_s$ conflict.
• Parallel: currents add.

4. Dual to Voltage Source

Voltage source ↔ current source are duals: $V$ fixed ↔ $I$ fixed; series $R_s$ ↔ parallel $R_p$; source transformation swaps them (next topic).

5. Worked Examples

(a) Ideal 2A source across 10Ω load: V=20V, P=40W delivered ✓

(b) Practical 2A source with Rp=10kΩ, load 1kΩ: equivalent: load voltage V= I_s·(Rp||RL)=2·(10k||1k)≈2·0.909k=1.818k? Actually compute: parallel 0.909k ⇒ V≈1.818V? Wait I_s·Rp||RL =2·0.909k=1.818kV? Error: 2A·0.909kΩ=1.818kV huge, but with Rp large, Rp||RL≈RL ⇒ V≈2·1k=2kV, current through load ≈1.818A (<2A) leaked through Rp 0.182A ✓

(c) Dependent: BJT collector: I_C = β I_B =100·0.01mA=1mA current source controlled by base current.

6. Exam Points

• Define ideal vs practical ($I=I_s - V/R_p$) — 5 marks, very frequent.
• Distinguish independent vs dependent — 3-5 marks.
• Show $I$ constant independent of $V$ — 3 marks.
• Parallel combination — 3 marks.
• Dual with voltage source — 3 marks.