OntheFrequencyResponseofStandardResistorsHPH8-94

c:QTmG_ca1Freq fo4.docV412/23/93,6/16/94,6/21/94,8/31/94hphFrequency Response of Standard ResistorsBasic Equivalent CircuitThe basic lumped-parameter equivalent circuit for a two-terminalresistor is that shown here.For this circuit:R +j@[L(1-@2LC)-R2c]Z=------------------=Rs+jXs[1](1-o2LC)2+(oRC)2Y-_Rtjo[R2c-L(1-02Lc)]=Gp Bp [2]R2+(oL)2From these we can get:Rand Rp R[1 (OL/R)2][3]&[4](1-o2LC)2+(oR.C)2and alsoQ=0[(L/R)(1-o2LC)-RC][5]If we neglect the 02Lc terms,we can see that (for this simple circuit)Rs is independent of L and decreases because of C,andRp is independent of c and increases because of L,andQ is positive (inductive)if R small and negative (capacitive)if R is large.The 02Lc terms are the beginnings of parallel resonance between L andlumped shunt c and usually very small even at 1 MHz except for wire-wound resistors,spool-wound types being particularly bad.However,these terms do cause the series resistance of low-valued 1442 resistorsto increase at much higher frequencies.Note that to cause an increasein Rs,L must be greater than R-C/2.Corrected Measurements (Open and Short Correction)Measurement results depend also on the OPEN and SHORT used for thecalibration of the fixture used.If we let Zsc joLs andYoc joCo then the formulas for corrected measurements on the simpleequivalent circuit are:R{1+o2红sCo)[6][1-o2红(C-Co)]2+[oR(C-Co)]2orRs=R{1+o2[2L(C-Co)-R2(C-Co)2])[6a]R[(1+02LsC)2 +02[(L-Ls 02LsLC)/R]2[7]{1+o2LsC0)orRp R{1 02 (L-Ls)2/R2])[7a]andQ o{(L-Ls+02LLsC)[1-@2L(C-Co)]/RR(C-Co)(1-02Lsc)}[8]orQ=[(L-Ls)/RR(C-Co)03L(L-Ls)(C-Co)/R[8a]where the simplified formulas assume 02Lsc is very small.