Low Current Measurements Series
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Number 100 Application Note Low Current Measurements Series induced by the voltage burden (or drop) across the entire amme- Basic Current Measurements ter model, and the uncertainty of the meter itself. In a typical circuit (see Figure 1a), a source causes a current (I) to flow through the circuit. The goal of any electrical current With measurements of currents in the normal range (typi- measurement is to insert an ammeter in series with the circuit so cally >1mA), errors caused by ammeter voltage burden, shunt that the current measured on the ammeter is identical to the cur- currents, and noise current are often small enough to be ignored. rent originally flowing through the circuit. To do so, the circuit In these cases, the displayed current reading is simply equal to is broken between points A and B, and the meter is connected the actual current plus or minus inherent meter uncertainty, (UM). as shown in Figure 1b. In the ideal case, the meter would have Meters designed to measure these normal currents generally con- absolutely no effect on the circuit. For practical measurements, sist of a voltmeter circuit that measures the voltage drop across however, several error sources may be present. These error a shunt resistor inserted in the series with the circuit being mea- sources can result in substantial uncertainty in the measurement, sured. (See the discussion on shunt ammeters that follows.) The as we will now discuss. reading provided by the voltmeter is thus directly proportional to the current flow. Any ammeter can be modeled to consist of the three sepa- rate circuit elements shown in Figure 1b: a shunt resistance (RSH) Unfortunately, the voltage burden (input voltage drop) pro- caused by the input cable connected to the meter; a generator of duced by such meters usually ranges from 200mV to about 2V. unwanted current (IC), which represents mainly currents generat- This voltage drop is sufficient to cause errors with current mea- ed by interconnections; and an internal resistance (RM), which surements below the normal range. To avoid such large voltage includes series cable resistance. Note that RM is in series with an drops, picoammeters and electrometers use a high gain amplifier ideal ammeter (MI), having no resistance or current source of with negative feedback for the input stage. As a result, the volt- its own. age burden is greatly reduced—on the order of 200µV or less. This low voltage burden reduces both measurement errors and Figure 1a: A source the minimum shunt cable resistance that must be maintained to causes a current (I) to Cable Shunt Generated Meter and Internal Resistance Currents Resistance flow through a wire provide a given meter accuracy. Consequently, no special mea- between A and B. sures need be taken to obtain unusually high cable resistance. RS IM RS A Typical picoammeters or electrometers that employ feed- IS I –15 I SH IC RM back ammeters generally provide sensitivities to 1fA (10 A) or V V V RSH M less and typical accuracy of 0.1% to 3%. MI B V I = Circuit Under Test Ammeter Shunt vs. Feedback Ammeters RS Equivalent Circuit Equivalent Circuit V VM ± IM = ISH IC UM There are two basic techniques for making low current measure- RS RS ments: the shunt method, and the feedback ammeter technique. Indicated Current Voltage Shunt Generated Meter Current to be Burden Current Current Uncertainty The shunt configuration is used primarily in DMMs (digital multi- Measured Error Error Error meters) and in older electrometers where cable capacitance causes Figure 1b: When an ammeter and connecting cable are used in place of a wire, a voltage burden (VM) is developed, which forces problems in the feedback mode. Picoammeters and newer elec- a shunt current (ISH) through the shunt resistance (RSH) of trometers use only the feedback ammeter configuration. The major the cable. Unwanted error currents (IE) are also generated due to various phenomena discussed in the text. difference between picoammeters and electrometers is that elec- trometers are multifunction instruments, while picoammeters mea- When the ammeter is connected in the circuit to be meas- sure only current. Also, a typical electrometer may have several ured, the current indicated on the meter is equal to the current decades better current sensitivity than the typical picoammeter. that would flow through the circuit without the ammeter inserted in the circuit, less errors caused by elements in the circuit model. Shunt Picoammeter These errors consist of current flowing through the model shunt Shunting the input of an electrometer voltmeter with a resistor resistance, currents generated by the interconnections, errors forms a shunt ammeter, as shown in Figure 2. The input current (I ) develops an input Circuit analysis shows that: IN Figure 2: Shunt ammeter voltage EIN across the E E + I R = E E = –AE , and E = – _____OUT shunt resistance OUT IN F IN OUT IN IN A (R ) as follows: – SHUNT A E 1 + _____OUT __ EIN = IINRSHUNT Thus, EOUT + IINRF = – and EOUT 1 + = –IINRF IIN RA A ( A ) Note that the voltage E _____OUT sensitivity of the circuit RSHUNT EIN E OUT Since A>>1, E = –I R and |E | = << E OUT IN F IN A OUT is controlled both by R B Note that the the value of RSHUNT Figure 4: Feedback ammeter with and the relative values amplifier gain can be selectable voltage gain changed as in the volt- of R and R . Thus, R A B RA + RB F E OUT = IIN RSHUNT R meter circuit, using the the output voltage ()B I IN combination shown in (EOUT) is given by: Figure 4. In this case, – R +R R +R A ________A B ________A B + EOUT = EIN = IINRSHUNT resistors RA and RB are R R R ( B )(B ) added to the feedback A EIN Although it might appear advantageous to use a larger loop, forming a multi- E OUT value for RSHUNT, there are actually several good reasons why plier. The gain of the RB RSHUNT should be made as small as possible. First, low value circuit is determined by resistors have better time and temperature stability, and a better the feedback resistor voltage coefficient than high value resistors. Second, low resistor and by the relative val- EOUT = –I RF (1 + RA + RB) values reduce the input time constant and result in faster instru- ues of RA and RB and ment response times. Finally, for circuit loading considerations, is given as follows: the input resistance RSHUNT of an ammeter should be small to R +R ________A B reduce the voltage burden EIN. EOUT = –IINRF ( RB ) However, using an electrometer (or any voltmeter) on its EOUT most sensitive range introduces noise and zero drift into the and again, E = – _____ IN A measurement. In contrast, Johnson noise current decreases as the value of RSHUNT increases. Thus, some compromise between these two opposing requirements is usually necessary. Choosing Sources of Current Errors a 1–2V full-scale sensitivity and the appropriate shunt resistance Errors in current-measuring instruments arise from extraneous value is often a good compromise. currents flowing through various circuit elements. In the model Feedback Picoammeter circuit of Figure 5, the current (IM), indicated on the meter, is actually equal to the current (I ) through the meter, plus addition- Figure 3 shows the 1 Figure 3: Feedback ammeter al meter uncertainty (U ). I is the signal current (I ), less shunt general configuration M 1 S current (I ) and the sum of all generated currents (I ). of a feedback type SH E ammeter. In this config- IIN RF Figure 5: Sources of current errors uration, the input cur- – A I rent (IIN) flows into the S Input E IN + E OUT Output input terminal of the I1 I1 = IS – ISH – IE amplifier (A), and it also flows through the VII I R I I feedback resistor (R ). SE CE SH RE IE F E OUT = –IINRF The low offset current M of the amplifier changes the current (IIN) by a negligible amount. Current Source IE = ISE + ICE + IRE + IIE Thus, the output voltage is a measure of the input current, IS = Source current RSH = Shunt resistance ISE = Source noise current IRE = Shunt resistance noise I = Interconnection noise current I = Instrument error current and sensitivity is determined by the feedback resistor (RF). The CE IE low voltage burden (EIN) and corresponding fast rise time are achieved by the high gain operational amplifier, which forces The circuit model shown in Figure 5 identifies various E to be nearly zero. IN noise and error currents generated during a typical current measurement. The ISE current generator represents noise currents generated within the source itself. These currents could arise due Figure 7: Piezoelectric effect to leakage, piezoelectric, or triboelectric effects, or through dielectric absorption. Applied Force Metal Terminal Similarly, the ICE current generator represents currents gen- I erated in the interconnection between the meter and the source + circuit. The same sources that generate noise currents in the cir- I cuit under test may produce noise in the interconnection. IRE is generated by the thermal activity of the shunt resistance and the rms value of the noise current and is given by: –– I = 4kTf/R RE SH Piezoelectric + Insulator Conductive Plate where: k = Boltzman’s constant (1.38 × 10–23J/K) T = absolute temperature in K Noise currents f = noise bandwidth in Hz Figure 8: Electrochemical effects also arise from electro- RSH = resistance in ohms Printed chemical effects, which Wiring Epoxy Printed Circuit Board Since peak-to-peak noise is about five times the rms value, the are shown in Figure 8. noise current can be ignored when measuring currents above 10–14A.