How can a single-ended signal be decomposed into common-mode and differential components?

Conditions

• Given the definitions of the differential signal and the common-mode signal.
• The system is linear, allowing superposition.

Reasoning, step by step

1. Recall the definition of the differential signal: $V_{diff} = V_1 - V_2$.
2. Recall the definition of the common-mode signal: $V_{comm} = \frac{1}{2}(V_1 + V_2)$.
3. Solve the system of linear equations to express $V_1$ and $V_2$ in terms of $V_{comm}$ and $V_{diff}$.
4. For the positive-polarity signal, the formula is $V_1 = V_{comm} + \frac{1}{2}V_{diff}$.
5. For the negative-polarity signal, the formula is $V_2 = V_{comm} - \frac{1}{2}V_{diff}$.

Example

The video verifies this decomposition using ADS simulation software. The synthesized signals $V_4 = V_{comm} + \frac{1}{2}V_{diff}$ and $V_5 = V_{comm} - \frac{1}{2}V_{diff}$ perfectly overlap with the original $V_1$ and $V_2$ waveforms.

Common misconceptions

• Thinking that the differential component is added in full rather than halved.
• Assuming this decomposition only applies to sinusoidal signals, whereas it applies to any time-domain waveform.

Watch the explanation

Explore next

• What is the mathematical definition of the differential signal?
• What is the mathematical definition of the common-mode signal?
• How does this decomposition help in analyzing signal integrity?