RMS-DC CONVERTERS. Mare Srbinovska, Cvetan Gavrovski

Transcription

1 ELECRONICS 6 September, Sozopol, BLGARIA RMS-DC CONVERERS Mare Srbinovska, Cvetan Gavrovski Faculty o Electrical Engineering and Inormation echnology, he Ss.Cyril and Methodius niversity P.O.Box 574, MK-1 Skopje, Republic o Macedonia mares@et.ukim.edu.mk, cvetang@et.ukim.edu.mk Abstract RMS or Root Mean Square is a undamental measurement o the magnitude o an AC signal. RMS converters are used in voltmeters or RMS voltage or current measurement. he principles o the computational method using the mathematical relation are mostly used in modern technology in integrated technique. But, the basic deinition or measuring true RMS value is deined as the amount o the power dissipated on known active load. rue RMS-DC converters can be built using pair o thermocouples. his solution has disadvantages due to the inertness o the thermocouples, that can be eliminated by substituting the thermocouples with diodes or transistors. In this paper are described RMS-DC converters, realized on the computational method and thermal conversion, the both methods are compared and in both cases are achieved similar results. 1. INRODCION Key words: RMS, converter, thermocouples he RMS value is a signiicant parameter which describes the energy content o a signal. RMS measurement techniques based on a signal s peak or average magnitude value may oer circuit simplicity but do not yield accurate results or nonsinusoidal signals. One popular technique or RMS measurement is the computational method, which uses the mathematical relation or determine the RMS voltage or current value. he other method uses thermal conversion, a technique or RMS measurement is to convert the energy o the signal to be measured into heat and then develop and measure the DC signal which produces an equal amount o heat. For example, an AC signal o 1V RMS will produce the same amount o heat in a 1V DC signal. rue RMS converters can perorm with high accuracy ±.5% (to 1MHz) and ± % (to 1MHz).. RMS-DC CONVERER BASED ON COMPAIONAL MEHOD RMS-DC converter based on the computational method is deined with the mathematical relation: 19

2 ELECRONICS 6 September, Sozopol, BLGARIA rms = 1 u dt his means squaring the signal, taking the average, and obtaining the square root, as it is shown on Figure 1. Fig. 1 Computational Method (Explicit method) he direct method o computation has a limited dynamic range because the stages ollowing the squarer must try to deal with a signal that various enormously in amplitude. hese practical limitations restrict this method to inputs which have a maximum o approximately 1:1 dynamic range. Generally better computing method uses eedback to perorm the square root unction indirectly at the input o the circuit as shown in Figure. Fig.. Computational method using eedback (Implicit method) Divided by the average o the output, the average signal levels now vary linearly with the RMS level o the input. his increases the dynamic range o this circuit as compared to explicit RMS circuits. AD637 converter uses an implicit method o RMS computation, has high accuracy, an extended requency response. On igures 3 and 4 are presented simulated output waveorms or dierent input waveorms(triangle and square input voltages) or AD637. his converter uses inverting low pass ilter stage to provide a buered output voltage whose averaging time constant is independent o the input signal level. he averaging time is the time in which the RMS converter holds the input signal during computation; it directly aects the accuracy o the RMS measurement. Fig. 3 Simulated output waveorm or triangle input waveorm 191

3 ELECRONICS 6 September, Sozopol, BLGARIA rue RMS measurement is a universal language among waveorms, allowing the magnitudes o all types o voltage or current waveorms to be compared to one another and to DC. hese converters are smart rectiiers; they provide an accurate RMS reading regardless o the type o waveorms being measured. Fig. 4 Simulated output waveorm or symmetrical square input waveorm As an example, i an average responding converter is calibrated to measure RMS value o sine-wave voltages, and then is used to measure either symmetrical square waves or DC voltages, the converter will have a computational error 11% higher than the true RMS value. 3. RE RMS-DC CONVERER BASED ON HERMAL CONVERSION In this paper is described a thermal technique o RMS measurement using resistortransistor chip; the base-emitter junction o a bipolar transistor is used to sense the change in temperature o the chip due to the power dissipated by a resistor (Figure 5). Fig.5 RMS-DC Converter using a pair resistor-transistor 19

4 ELECRONICS 6 September, Sozopol, BLGARIA he power dissipated by the heater resistor R1 due to the input signal i heats the input pair producing change in the base-emitter voltage o 1. his generates an error voltage which is ampliied by the operational ampliier A 1, so the output voltage heats the resistor R. In moment when the potentials o the operational ampliier dierential input are equal, the circuit is in equilibrium so rms = irms. hen DC output voltage is proportional to the AC input voltage. From the Ebers - Moll relationship or orward biased junction S V k I is the saturation current. I I E BE = ln, (1) q I S 3 αvbo / k S = B e, () By combining (1) and () the junction equation can be written in terms o the physical constants and the base-emitter voltage at a speciic emitter current and temperature ( I E and ). 3 k I E V BE ln + + q I E V BE = Vb at I E and ( VBE Vb ) Vb = (3) Dierentiating (3) with respect to temperature yields the junction temperature coeicient, and or constant emitter current is dv BE VBE Vb 3k = + I = const 1 ln (4) E d q he temperature coeicient is mv / C and to have nonlinearity o less than % or temperature between and 1 C. Neglecting the eects o the sense transistor base currents in the base resistors R b, the base-emitter voltages o the sense transistors can be related as Vbe 1 = Vbe + H( s) (5) where H(s) is the AC eedback transer unction: srbc A H = 1+ sc ( Rb + R ) (6) Combining (5) and (6) yields A 1(1 + s τ ) i VBE1 VBE = + (7) A (1 + s τ ) 1+ sτ A where A is the thermal gain o the transistors. Its typical value is A = 1 mv / V, and τ is thermal time constant. τ is a ilter time constant deined as: RbC A τ = (8) A 193

5 ELECRONICS 6 September, Sozopol, BLGARIA he requency dependence o the RMS-DC converter may be nonlinear since the transer unction time constant is inversely proportional to the output voltage i A is linear. his nonlinear requency dependence produces an unsymmetrical step response and a low requency cuto or accurate RMS converter which is proportional to the RMS value o the input. hese characteristics are undesirable i ast response is necessary and a nonlinear AC eedback should be employed. By making A a square law ampliier Au = ρ u (9) he time constant will be independent o the output; combining (8) and (9) the ilter time constant or square law A, τ s is RbC ρ τ s = (1) A For sinusoidal inputs ui = irms cosωt, the output as a unction o the input requency is 1/ ( ) + ω τ u t = 1 cos irms + ωt (11) ( )( 1 4 ) + ω τ + ω τ s his is valid only or ilter time constant which has square law ampliier Au = ρ u, as it is shown on igure 6b. However, an approximate solution or linear A can be obtained by relating the output o the linear ampliier to that o the square law ampliier = A ac = A ac or linear A (1) = ρ ac ρ dc ac or square law A (13) he RMS value o the ripple at the output is then A Edc Eirms ripple = linear A (14) 8πR C A ripple b 1/ A Eirms = square law A (15) 16πR C ρ b In igure 6(a) the RMS value o the output ripple is simulated versus the RMS value o the input or an input requency o Hz. As, expected, the output ripple with linear AC eedback is proportional to the square o the RMS value o the input where it is linearly proportional to the RMS value o the input with square law AC eedback. he square law does, thereore, provide a low requency cuto which is independent o the signal level. 194

6 ELECRONICS 6 September, Sozopol, BLGARIA Fig.6 (a) Output ripple versus input or a Hz input or both linear and square A (b) Output voltage as a unction o time or sinusoidal input signal R = 1kΩ, C = μf, and A = or A =. ) b 5 4. CONCLSION Some advantages o implicit computation (AD637) over other methods are ewer components, greater dynamic range and generally low cost. A disadvantage has less bandwidth than either thermal or explicit method. rue RMS-DC converters are capable o producing high accuracy over a wide range o levels, waveorms and requencies. 5. REFERENCES: [1] Analog Devices, rue RMS-DC Converter AD637, datasheet, 1999,SA. [] William E.Ott, A new technique o hermal RMS measurement, IEEE journal o solid state circuit, N.6, December [3] Euisik Yoon and Kensall D.Wise, A wideband monolithic RMS-DC converter using micromachined diaphragm structures, IEEE transactions on electron devices, N. 9 September [4] Erno H.Klaassen, Richard J.Reay, and Gregory.A.Kovacs, Diode based thermal RMS converter with on-chip circuitry abricated using standard CMOS technology. [5] W. Jackson, hin-film / Semiconductor hermocouple or Microwave Power Measurements, HP Journal, pp. 16-3, Sept