Lumped Circuit vs Distributed Circuit
The difference between lumped and distributed circuits comes down to how voltage, current, and physical size relate to the signal wavelength.
Lumped Circuit
Concept: Components are assumed to be concentrated at discrete points.
Condition:
\[ \text{Size of circuit} \ll \lambda \]
Where \( \lambda \) is the wavelength of the signal.
Assumptions:
- Voltage and current are uniform across components
- No propagation delay
Governing Laws:
- Ohm's Law: \( V = IR \)
- Kirchhoff’s Laws (KVL and KCL)
Examples:
- DC circuits
- Low-frequency AC circuits
- Basic electronic circuits
Distributed Circuit
Concept: Electrical parameters are distributed continuously along the conductor.
Condition:
\[ \text{Size of circuit} \approx \lambda \ \text{or larger} \]
Characteristics:
- Voltage and current vary with position and time
- Propagation delay is significant
Telegrapher’s Equations:
\[ \frac{\partial V(x,t)}{\partial x} = -L \frac{\partial I(x,t)}{\partial t} - RI(x,t) \]
\[ \frac{\partial I(x,t)}{\partial x} = -C \frac{\partial V(x,t)}{\partial t} - GV(x,t) \]
Examples:
- Transmission lines
- Coaxial cables
- Microwave circuits
- Antennas
Differences
| Feature | Lumped Circuit | Distributed Circuit |
|---|---|---|
| Size vs Wavelength | \( \ll \lambda \) | \( \approx \lambda \) or larger |
| Parameters | Discrete | Continuous |
| Voltage/Current | Uniform | Varies with position |
| Time Delay | Ignored | Important |
| Analysis | Algebraic equations | Partial differential equations |
- Lumped: Instant response (small system)
- Distributed: Signal travels like a wave (large system)