An oscilloscope shows ringing at the rising edge of a digital signal at approximately 50,text MHz . To identify the resonant inductance if stray capacitance is estimated at 10,text pF , use f_r = frac 1 2pisqrt LC . The stray inductance is approximately:

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Electronics Engineering QUESTION #11742

Question 1

An oscilloscope shows ringing at the rising edge of a digital signal at approximately $50\,\text{MHz}$. To identify the resonant inductance if stray capacitance is estimated at $10\,\text{pF}$, use $f_r = \frac{1}{2\pi\sqrt{LC}}$. The stray inductance is approximately:

$1.0\,\text{nH}$
$10\,\text{nH}$✔️
$1.0\,\mu\text{H}$
$100\,\text{nH}$

Correct Answer Explanation

Rearranging: $L = \dfrac{1}{(2\pi f_r)^2 C} = \dfrac{1}{(2\pi \times 50\times10^6)^2 \times 10\times10^{-12}} = \dfrac{1}{(3.14\times10^8)^2 \times 10^{-11}} = \dfrac{1}{9.87\times10^{16} \times 10^{-11}} = \dfrac{1}{9.87\times10^6} \approx \mathbf{10.1\,\text{nH}}$. This stray inductance (from PCB traces, via stubs, or lead inductance) causes ringing and EMI issues in high-speed digital and power circuits.

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