# Task 6.9: Measuring RMS Values
>[!table] Table I: Measured RMS Voltage & Signal Frequency (Triangular Waveform)
>| Measurement | Value |
|---|---|
| RMS Voltage [V] | 1.741 |
| Frequency [Hz] | 1000 |
>[!calculation] RMS Calculation for Triangular Wave
>
For a triangular waveform with peak amplitude ($V_p$):
>
$V_{RMS,AC}=\frac{V_p}{\sqrt{3}}$
>
Given:
>
$V_p=3V$
>
$V_{RMS,AC}=\frac{3}{\sqrt{3}}=1.732V$
>
DC offset:
>
$V_{DC}=2V$
>[!table] Table II: Calculated vs Measured RMS Voltage (Triangular Waveform)
>| Quantity | Value |
|---|---|
| Calculated AC RMS [V] | 1.732 |
| Calculated DC RMS [V] | 2.000 |
| Measured RMS [V] | 1.741 |
| Percent Error | 0.52% |
<div style="page-break-after: always;"></div>
>[!calculation] Percent Error
>
$\%\text{ error} = \frac{|V_{meas}-V_{calc}|}{V_{calc}}\times100$
>
$\%\text{ error} = \frac{|1.741-1.732|}{1.732}\times100$
>
$=0.52\%$
>[!figures] Figure I: Oscilloscope Display of Triangular Waveform Used for RMS Measurement
>![[Pasted image 20260304212447.png|center|500]]
>[!table] Table III: Measured RMS Voltage & Frequency (Sinusoidal Waveform)
>| Measurement | Value |
|---|---|
| RMS Voltage [V] | 1.419 |
| Frequency [Hz] | 999.2 |
<div style="page-break-after: always;"></div>
>[!calculation] RMS Calculation for Sinusoidal Wave
>
For a sinusoidal waveform:
>
$V_{RMS,AC}=\frac{V_p}{\sqrt{2}}$
>
Given:
>
$V_p=2V$
>
$V_{RMS,AC}=\frac{2}{\sqrt{2}}=1.414V$
>
Total RMS including DC offset:
>
$V_{RMS,total}=\sqrt{V_{AC}^2+V_{DC}^2}=\sqrt{(1.414)^2+(4)^2}=4.243V$
>[!table] Table IV: Calculated vs Measured RMS Voltage (Sinusoidal Waveform)
>| Quantity | Value |
|---|---|
| Calculated AC RMS [V] | 1.414 |
| Calculated Total RMS [V] | 4.243 |
| Measured RMS [V] | 1.419 |
| Percent Error | 0.35% |
>[!calculation] Percent Error
>
$\%\text{ error} = \frac{|1.419-1.414|}{1.414}\times100$
>
$=0.35\%$
<div style="page-break-after: always;"></div>
>[!figures] Figure II: Oscilloscope Display of Sinusoidal Waveform Used for RMS Verification
>![[Pasted image 20260304212525.png|center|500]]
---
# Task 6.10: Hi-Z vs 50Ω on Function Generator
>[!table] Table V: Measured RMS Voltage for Different Generator Modes
>| Load Resistance | Hi-Z Mode RMS Voltage [V] | 50Ω Mode RMS Voltage [V] |
|---|---|---|
| 1kΩ | 0.673 | 0.341 |
| 47Ω | 1.348 | 0.682 |
>[!calculation] Function Generator Internal Impedance Model
>
The function generator behaves like an ideal voltage source with a $50\Omega$ internal series resistance.
>
When connected to a load ($R_L$), the output forms a voltage divider:
>
$V_{out}=V_s\frac{R_L}{R_L+50}$
>
For large loads ($R_L\gg50\Omega$):
>
$V_{out}\approx V_s$
>
For loads comparable to $50\Omega$, significant voltage division occurs.
---
<div style="page-break-after: always;"></div>
# Task 6.11: Superposition of Waves
>[!figures] Figure III: Superposition Test Circuit
>![[Pasted image 20260304212553.png|center|500]]
>[!figures] Figure IV: Combined Waveform from Two Input Signals
>![[Pasted image 20260304212602.png|center|500]]