Thévenin and Norton equivalent calculator
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Result
Find the Thévenin and Norton equivalents of a DC circuit between two terminals. Describe the circuit as a short netlist of resistors, voltage sources and current sources. The calculator writes the nodal equations, solves them for the open-circuit voltage Vth, turns the sources off to find Rth, and gives the Norton current In and the maximum power a load could draw.
Step-by-step solution
Nodal analysis of the circuit
Node voltages
Thévenin resistance
Norton equivalent
Key formulas
- Thévenin voltage
- Vth = Vopen circuit
- Thévenin resistance
- Rth: all sources off, seen from a–b
- Norton current
- IN = Vth/Rth
- Load current
- IL = Vth/(Rth + RL)
- Maximum power transfer
- RL = Rth, Pmax = Vth²/(4Rth)
How to find a Thévenin equivalent
- Remove the load and find the open-circuit voltage between the terminals A and B: Vth = V_A − V_B.
- Turn off the independent sources: replace voltage sources by short circuits and current sources by open circuits.
- Find the resistance seen between A and B: that is Rth. With a test source: Rth = V_test/I_test.
- Norton: In = Vth/Rth, with the same Rth in parallel.
- Maximum power transfer: a load RL = Rth receives Vth²/(4Rth).
Questions and answers
How do I write the netlist?
One element per line or separated by semicolons: a name starting with R, V or I, two node names and a value, for example R1 a b 4k. Node 0 (or gnd) is ground. For V1 a b 12 the + terminal is at a. For I1 a b 2 the 2 A flows through the source from a to b, so it enters the circuit at b.
Can I use unit prefixes?
Yes: k for kilo, meg or M for mega, m for milli, u or µ for micro, n for nano and p for pico. 4.7k means 4700 Ω. Note that SPICE reads M as milli; here M means mega, so meg is the safest way to write mega.
Why does the calculator use a test current for Rth?
Combining resistors in series and parallel only works for simple circuits. Injecting 1 A into terminal A with all sources off always works: the voltage that appears across the terminals equals Rth.
Are dependent sources supported?
No, only resistors and independent voltage and current sources. With dependent sources Rth must be found with a test source while the dependent sources stay on.
What if Rth comes out as 0?
Then an ideal voltage source sits directly across the terminals. The Thévenin equivalent is just that source, and a Norton equivalent does not exist.
Practise it yourself
Practise Thévenin & Norton
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.