Shunt capacitance of 1206 SMD resistors

Fig.1: Equivalent circuit of the setup.

To assess their parasitic shunt capacitance, size 1206 SMD resistors with values from 100 Ω to 1 MΩ were connected in series between two SMA-connectors. An HP8753D network analyzer (NA) was used to acquire S₂₁, from which the shunt capacitance can be calculated. The equivalent circuit of the the setup is as shown in Fig.1. Z_T is the resistor under test. Depending on its value, beyond a certain frequency, its impedance is expected to become capacitive, which shows up as a slope of the S₂₁ curve of +20dB/decade.

The transfer function of the equivalent circuit is:

(1)

Since Z_T is mostly much larger than both R_S and R_l, this simplifies to U₂/U_s=R_l/Z_T for most of the curves in the plot of Fig.2. The NA expects its source port to be terminated into 50 Ω, and displays 0dB for Z_T=0. It displays in fact 20log(U₂/U_s)+6.

Fig.2: S21 curves for 1206 SMD resistors.

Fig.2 shows the obtained S₂₁ curves. The sloping black line corresponds to Z_T an ideal 50 fF capacitor. In conclusion, the shunt capacitance of 1206-size SMD resistors is about 50 fF, indendent of their value. For values of 100 Ω and below, the series inductance is more important than the shunt capacitance.

Fig.3: Simulation and actual resistor compared

Fig.3 shows a comparison of an ideal 1 MΩ//50fF (blue curve) with the actual measurement (red curve). Clearly, in the transition region between the resistive and capacitive behaviours, the actual resistor has a marginally lower impedance than its ideal model. The curves move apart by a little over 1dB, corresponding to about 10% difference in impedance. At the high-frequency end, the red line curves up due to the effect of parasitic series inductance. At the low-frequency end, it also curves up, for reasons I do not currently understand. If I insert a few dB of attenuation at both ends of my test jig, the effect goes away.

If someone wants to play with the data, the files are available as, e.g., http://cern.ch/jeroen/resistor/1M.dat. The file format is text, 201 lines times two columns. First column is frequency in Hz and 2nd column is magnitude in dB. You can guess the names of the files for the other resistance values.