# Conducted Emissions testing

-February 04, 2013

A negative resistance element is capable of serving as an amplifier. A switchmode power supply of extremely high efficiency has a negative dynamic input impedance.

( Please see my Switchmode dynamic impedance article on LICN )

That negative impedance can have an amplifying effect which can act on whatever stray signals and noise that are coming in on the power line. Testing of a switchmode power supply for its own conducted emissions can be compromised by this.

We first look at the concept of amplification by a negative resistance in its simplest form by examining a voltage divider.

We then look at this concept in real world action. In the left image below, a set of frequency comb lines is seen on our spectrum analyzer when we're testing for the "conducted emissions" of a table lamp. The lamp is obviously not the source of that spectra. But then, when the lamp is replaced by a switchmode power supply, the comb lines show up very much higher on the analyzer display. This is not a good thing.

Power lines can be carrying unexpected signals. For example, I have been told that these comb lines may be coming from signals deliberately placed on the power line by the utility company as part of a data carrying load management system. Whatever their cause, since they are there and cannot be removed, the question to ask is, do you have some really good power line filtering in place for their removal from your test results? If not, do you have a very clean, on-site line power generator of your own?

We now look at an analysis of the effect of having a negative load impedance when using a typical line impedance stabilization network (LISN) for conducted emissions testing. We begin  with this algebraic analysis of the transfer function from the power line to the spectrum analyzer:

We then use this last equation to look at the transfer function from the power line to the spectrum analyzer versus the value of the load, R2 for both positive and negative values of R2. Then we also make a SPICE model and when we compare the outcomes, we find that they agree:

We find that the signal attenuation that is normally expected of the LISN from the power line to the spectrum analyzer can be totally lost above some particular corner frequency.  In such a case, unwanted signals coming in on the power line and appearing on the spectrum analyzer, which may very possibly be above the conducted emssion limits for the UUT, can be falsely attributed to an innocent UUT.

The complexity of this effect can be intimidating. If we look at a few different load values while still assuming them to be constant over all frequencies, we see tremendous variability in the degree of harm to the LISN transfer function as follows:

The dynamic impedance presented by the UUT is not at all likely to be a constant value over our entire reange of frequencies. Try now to imagine what these curves would look like if the load impedance were to vary as a function of frequency. It boggles the imagination. However, a diminished capability of the LISN to filter out power line signals would still be an issue.

Just in case you'd like to play around with the above algebraic analysis, this is the GWBASIC code (Yes, I still use it.) for doing that. Run it under Windows 98SE or earlier. On some machines, it will also work with Windows XP, but not on all machines.

10 CLS:SCREEN 9:COLOR 15,1:YSTART=240:XSTART=40:PI=3.14159265#

20 PRINT "save "+CHR\$(34)+"lisnrneg.bas"+CHR\$(34):PRINT:ON ERROR GOTO 270

30 PRINT "save "+CHR\$(34)+"a:\lisnrneg.bas"+CHR\$(34):PRINT:PRINT

40 C\$="###ê Load ###.# dB":D\$="100 Hz to 100 MHz":FDBHOLD=1000000!

50 KK=0:F=100:FOR HX=0 TO 40:HDB=-HX:GOSUB 190:XHOLD=X:X=X+2

60 IF ABS(HX-5*INT(HX/5))<.01 THEN X=X+4

70 IF ABS(HX-10*INT(HX/10))<.01 THEN X=X+4

80 GOSUB 200:X=XHOLD:GOSUB 200:NEXT HX:KK=0

90 FOR FX=2 TO 7:FOR FY=1 TO 10:F=FY*10^FX:HDB=-39.99:GOSUB 190:YHOLD=Y:Y=Y+4

100 IF ABS((FY-1)*(FY-10))<.01 THEN Y=Y+4

110 GOSUB 200:Y=YHOLD:GOSUB 200:NEXT FY:NEXT FX:KK=0

120 PRINT D\$:PRINT:PRINT FDBHOLD/1000000!;"MHz":PRINT:GOTO 240

130 REM

140 REM Transfer function subroutine

150 W=2*PI*F:DR=(R1+R2)-W^2*L1*C1*(R2+R3):DI=W*(L1+C1*(R1*R2+R2*R3+R1*R3))

160 DEN=SQR(DR^2+DI^2):NUM=W*R2*R3*C1:H=ABS(NUM/DEN)

170 HDB=20*LOG(H)/LOG(10):IF ABS(F-FDBHOLD)<100 THEN HDBHOLD=HDB

180 RETURN

190 X=30*LOG(F):Y=HDB*5:IF HDB<-40 THEN KK=0

200 CC=XSTART+X:DD=(320-Y-YSTART):IF KK<>0 THEN LINE (AA,BB)-(CC,DD)

210 AA=CC:BB=DD:KK=1:RETURN

220 COLOR 15-CT,1:FOR FX=2 TO 7:FOR FY=1 TO 10 STEP .01:F=FY*10^FX

230 GOSUB 150:GOSUB 190:NEXT FY:NEXT FX:KK=0:RETURN

250 READ R2:GOSUB 220:CT=CT+1:IF CT>5 THEN CT=1

260 PRINT USING C\$;R2,HDBHOLD:GOTO 250

270 RESUME 280

280 COLOR 15,1:DATA 50,10,2,-30,-45,-49,-50:REM Load values