The Paperclip Probe

High Frequency Measurements Web Page
Douglas C. Smith

Address: P. O. Box 1457, Los Gatos, CA 95031
TEL:      800-323-3956/408-356-4186
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Email:    doug@dsmith.org

Using a Paper Clip to Measure Signals and Noise

In the picture above, a paper clip (any stiff wire will do) is bent into a square shape and covered with insulation, forming an unshielded magnetic loop probe. Such a structure can be quite useful in circuit troubleshooting and noise investigations. A conductor carrying a current, i, will have a voltage drop across it given by:

e₁ = Ldi/dt + Ri

where:

L is the inductance per unit length of the conductor
R is the resistance per unit length
e₁ is the voltage drop per unit length
the unit length is small compared to a wavelength at the highest frequency of interest (electrically short)

At frequencies above a few hundreds of kHz, the resistive component becomes negligible and the equation simplifies to just:

e₁ = Ldi/dt

A conductor nearby the current carrying conductor, such as a side of the square loop above, will pickup an open circuit voltage of:

e₂ = Mdi/dt

where:

M is the mutual inductance between the current carrying wire and the nearby wire per unit length.

Since L and M are constants, then e₁ and e₂ are only different by a constant. M must be smaller than L for two parallel wires (due to the magnetic flux that flows between the wires instead of enclosing both), so e₁ is a lower bound estimate for the magnitude of e₂ and has the same wave shape.

Using this principle, a simple square loop, such as the one above, can be used to estimate the voltage drop across conductors. When the probe is held up to a conductor carrying high frequency current, the probe's open circuit output voltage is a lower bound for the voltage between the corners of the probe along the current carrying conductor.

The probe should be connected to a oscilloscope or spectrum analyzer using a coaxial cable terminated in its characteristic impedance. This resistive load on the loop in combination with the self inductance of the loop form a low pass filter on the probe output. For a loop with sides of 1 cm, this corner frequency will be between 200 and 300 MHz.

Possible uses are estimating the drop across bonding wires and lead frames of integrated circuits or measuring noise effects on a printed wiring board. My paper in the 1999 IEEE EMC Symposium Proceedings discusses such uses of magnetic loops in more detail as well as the theory and limitations of such probes.

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Questions or suggestions? Contact me at doug@dsmith.org