LCR Meters - Stanford Research Systems - #5

All non-ideal passive devices (resistors, inductors and capacitors) can be modeled as a real component (resistor) either in series or in parallel with an imaginary component (capacitor or inductor). The impedance of these components

ESR (equivalent series resistance) can be measured. The equivalent series resistance in capacitors includes effects like dielectric absorption in addition to the ohmic losses due to leads. It is often listed on data sheets for electrolytic capacitors

change as a function of frequency. The series and parallel models are mathematically equivalent and can be transformed back and forth with the equations shown. The SR715 and SR720 can switch between either parallel or series equivalent circuits.

Usually one model is a better representation of the device under operating conditions. The most accurate model depends on the device and the operating frequency. Certain devices are tested under conditions defined by the manufacturer or by industry standards. For example, electrolytic capacitors are often measured in series at 120 Hz in the C+R mode, so the

used in switching power supplies. At high frequencies, the ESR is the limiting factor in the performance of the capacitor.

The quality factor (Q) is the ratio of the imaginary impedance to the real impedance. For inductors, a high Q indicates a more reactively pure component. A low Q indicates a substantial series resistor. Q varies with frequency. With resistors, often all that is stated is that the resistor has low inductance.

The dissipation factor (D) is equal to 1/Q and is the ratio of the real impedance to the imaginary impedance. A low D indicates a nearly pure capacitor. D is commonly used when describing capacitors of all types.

Z_s = R_s - j — = — (D - j) = R_s ⁽1- ^{j p} 1 + jraR_pC_p 1 + D²

R_p fflL

Q =

Q

fflL_p R_s

D

1

(oFlpOp

D = roRC

Q

L =-L R =— R = QfflL

^s 1 + Q^{2 p s} Q ^pp

11

R =— B =--^p G ^p ML

D² 1 + D²

C_s = (1 + D² )C_p

Y = ^Gp + j mCp

Y = G