Common-mode voltage (\(V_{cm}\)) represents the average voltage of two signal lines with respect to a common reference point, typically ground. It is essential in differential signal systems, power electronics, and EMC testing.

The common-mode voltage is mathematically defined as:
\(V_{cm} = \frac{V_+ + V_-}{2}\)

Where:
- \(V_+\) is the voltage on the positive signal line relative to ground
- \(V_-\) is the voltage on the negative signal line relative to ground

To measure Vcm:

• Oscilloscope: Connect probes to \(V_+\) and \(V_-\), measure each with respect to ground, and compute the average.
• Differential Probe: Use to extract both differential and common-mode signals.
• Multimeter: For DC or low-frequency, measure \(V_+\) and \(V_-\) relative to ground and average them.

Measuring Vcm helps identify noise, verify balance, and improve performance.

Common-mode impedance (\(Z_{cm}\)) is the impedance that common-mode currents encounter between signal lines and ground.

To measure \(Z_{cm}\) accurately, use an impedance analyzer (e.g., Keysight E4990A). Connect the two signal lines together to form a common-mode path, then measure the impedance between this node and ground.

Alternatively, use a Vector Network Analyzer (VNA) with a mode-conversion setup to measure \(Z_{cm}\) using mixed-mode S-parameters.

For a basic estimation, inject a common-mode signal into the system and measure voltage and current. Then calculate:
\(Z_{cm} = \frac{V_{cm}}{I_{cm}}\)

Proper grounding and shielding are essential to reduce noise and ensure accurate readings.

Insertion Loss (IL) is a fundamental parameter used to describe how much signal power is lost when a component, such as a filter, connector, or cable, is inserted into a transmission path. It is typically expressed in decibels (dB) and is crucial in high-frequency, RF, and communication systems, where maintaining signal strength and quality is important.

The insertion loss quantifies the difference in signal amplitude or power before and after the device under test (DUT). The voltage-based formula for insertion loss is:
\(\text{Insertion Loss (dB)} = 20 \log_{10} \left( \frac{V_{\text{in}}}{V_{\text{out}}} \right)\)

Where:
\(V_{\text{in}}\) is the voltage before the DUT
\(V_{\text{out}}\) is the voltage after the DUT

For power-based measurements, the equation becomes:
\(\text{Insertion Loss (dB)} = 10 \log_{10} \left( \frac{P_{\text{in}}}{P_{\text{out}}} \right)\)

A higher insertion loss indicates greater signal attenuation. For example, an insertion loss of 3 dB means approximately 50% of the power is lost. Insertion loss is often measured using a Vector Network Analyzer (VNA), which directly measures transmission parameters such as S21.