# Prelab Calculations
- Equivalent Resistance $R_{eq}=324.429\Omega$
- Thevenin Voltage $V_{oc}=2.357V$
- Norton Current $I_{sc}=7.266\Omega$
# Task 3.8: Complete Nodal Analysis
>[!figures] Figure I: Full LTSpice Circuit
>![[Pasted image 20260218153537.png|center|500]]
>[!figures] Figure II: LTSpice Circuit Values Relative to Ground
>![[Pasted image 20260218162712.png|center|500]]
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> [!table] Table I: Measured Node Voltages Relative to Ground
> | Node | Voltage [V] |
|-----|-----|
| A | 1.915 |
| B | 0.540 |
| C | 1.159 |
| D | 1.687 |
| E | 1.299 |
>[!table] Table II: Measured Currents Through Circuit Components
>| Component | Current [mA] |
|-----|-----|
| R1 | 8.564 |
| R2 | 3.435 |
| R3 | 3.486 |
| R4 | 4.559 |
| R5 | 8.003 |
| Vs | 7.794 |
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# Task 3.9: Equivalent Circuits
>[!figures] Figure II: Thevenin (left) and Norton (right) Equivalent Circuits
> ![[Pasted image 20260218154325.png|300]] ![[Pasted image 20260218154333.png|352]]
>[!figures] Thevenin (above) and Norton (below) LTSpice Data
>![[Pasted image 20260218154854.png|center|500]]
>![[Pasted image 20260218154904.png|center|500]]
>[!calculation] Thevenin & Norton Circuit Values
>
$I_{L}=\frac{V_{th}}{R_{th}+R_{L}}=\frac{2.357}{656.34}=0.003591A=3.591mA$
$V_{L}=I_{L}R_{L}=0.003591\cdot330=1.185V$
>[!table] Measured Values in Thevenin Circuit
>| Measurement | Thevenin Value |
| ------------- | -------------- |
| $V_{oc}~[V]$ | 1.153 |
| $I_{SC}~[mA]$ | 3.437 |
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> [!calculation] Thevenin Measurement %errors
> $\text{\%error}_{1}=100 \left|\frac{1.153-1.185}{1.185}\right|=2.70\%$
> $\text{\%error}_{2}=100 \left|\frac{3.437-3.591}{3.591}\right|=4.29\%$
>[!table] Resistor Load Voltage & Current Measurements, Equivalent and Original Circuits
>
| Load [Ω] | $V_{load}$ [V] (Original) | $V_{load}$ [V] (Equivalent) | $I_{load}$ [mA] (Original) | $I_{load}$ [mA] (Equivalent) |
| -------: | ------------------------: | --------------------------: | -------------------------: | ---------------------------: |
| 100 | 0.543 | 0.719 | 5.429 | 7.209 |
| 1,000 | 1.736 | 1.917 | 1.755 | 1.931 |
| 10,000 | 2.238 | 2.302 | 0.226 | 0.232 |
>[!calculation] Original & Equivalent Circuit %errors
> ##### $V_{Load}\text{ \%error calculations}$
> $\%\text{error}_{100\Omega}=100 \left|\frac{0.719-0.543}{0.543}\right|=32.4\%$
> $\%\text{error}_{1k\Omega}=100 \left|\frac{1.917-1.736}{1.736}\right|=10.42\%$
$\%\text{error}_{10k\Omega}=100 \left|\frac{2.302-2.238}{2.238}\right|=2.86\%$
> ##### $I_{Load}\text{ \%error calculations}$
> $\%\text{error}_{100\Omega}=100 \left|\frac{7.209-5.429}{5.429}\right|=32.79\%$
$\%\text{error}_{1k\Omega}=100 \left|\frac{1.931-1.755}{1.755}\right|=10.03\%$
$\%\text{error}_{10k\Omega}=100 \left|\frac{0.232-0.226}{0.226}\right|=2.65\%$