Finding Thevenin equivalent

MATLABparalleltheveninvoltage

I'm looking to find the Thevenin equivalent of two parallel voltage sources where each source has some internal resistance as well for simulation in Matlab. I don't know where and how exactly to put a voltage meter and current meter in place to measure the open source voltage and short circuit current. Can anyone guide me?

Best Answer

OK, say we have an unknown circuit and we want to measure its Thevenin equivalent:

Thevenin equivalent with load resistor

We have a resistive load \$R_L\$ connected to our circuit and we don't want to remove it while measuring the necessary quantities. First we measure the short-circuit current by connecting an ammeter between the measurement node and ground. The ammeter will short-circuit the load, which is exactly what we want in order to measure the short-circuit current. Let's call the result of our measurement \$I_{Th}\$. This current defines the ratio of \$V_{Th}\$ and \$R_{Th}\$: $$I_{Th}=\frac{V_{Th}}{R_{Th}} \tag{1}$$

Since we cannot remove the load, we cannot directly measure the open-circuit voltage \$V_{Th}\$. Instead, we measure the voltage \$V_L\$ across the load. The current through the load is then

$$I_L=\frac{V_L}{R_L}=\frac{V_{Th}}{R_{Th}+R_L} \tag{2}$$

Equations (1) and (2) allow us to solve for the unknown quantities \$V_{Th}\$ and \$R_{Th}\$:

$$V_{Th} = \frac{V_LR_LI_{Th}}{I_{Th}R_L-V_L}$$

$$R_{Th} = \frac{V_LR_L}{I_{Th}R_L-V_L}$$

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