VK-8 RMS CONVERTER |

The used conversion method is based on the thermal action of an alternating current. Average power dissipated in a heater doesn't depend on frequency and waveform of the flowing current, it exactly corresponds only to the root-mean-square value of this current. To measure the RMS value of an AC voltage, it first should be converted to current and for that an input amplifier usually is necessary. Just its broadband capability defines the upper frequency limit of the carried out RMS measurement and figures up to 100MHz are here quite attainable. Thermo-couple is the most widespread element to sense the heating and produce an output DC signal for further processing, but the faced difficulties in this case often outweigh the virtue of handling broadband signals of heavily distorted waveform. The disadvantages include a considerable, up to 5s thermal inertia, low (not exceeding 20mV) DC output level, restricted (10dB) range of input AC voltages and at last square-law transfer characteristic. The latter can be linearized with the help of the second thermo-couple and heater operating in DC conditions, but here the necessity of matching the two thermo-devices arises. In this design, the above problems are solved by using a single optocoupler whose lamp turns heating to light which acts on a photoresistor, the DC voltage across that resistor then being compared with a reference level (not necessarily stable). As a key converting element, this optocoupler has a satisfactory settling time (less than 1s) and high output signal level (about 1,5V), it is supplied in turn by short alternating and direct current injections. Each of these currents is controlled effectively and independently, but is determined by the same, mentioned-above reference, therefore their RMS values always will be set and then with high accuracy maintained equal, even in conditions of variable temperature, supply voltages etc. Current at which this thermal equilibrium is achieved is chosen about 10mA, close to its optimum for the given opto device. CIRCUIT OPERATION The simplified circuit diagram of the RMS converter is represented in Fig.1. Fig.1. RMS converter - simplified circuit diagram. Input AC voltage V _{INA} is buffered (A_{1}), attenuated
(R_{1}, R_{2}) and then amplified (A_{2}). The
output alternating current I_{OUTA} is fed through the closed
S_{1A}, S_{1B} to a switchable load L which does not
influence this current, as the gain defining network (R_{4},
R_{5}) takes the feedback voltage sample from a stable resistor
R_{01}. Assuming that A_{1} and A_{2} are ideal
op amps, the relationship between I_{OUTA} and V_{INA}
can be written as:During this so-called AC phase of operation lasting about 0,7s, the Q output of generator G (point A) goes low and the state of associated analogue switches is following: S _{1A}, S_{1B},
S_{3B} are closed and S_{2A}, S_{2B},
S_{3A} - open. At that time the above alternating current
I_{OUTA} flows through the filament lamp L which sends light to
a photoresistor R_{L2}, the optocoupler output V_{D}
being taken from point D.The set reference V _{REF} (about 1,5V) is compared with
V_{D} at the inverting input of A_{5} and their
difference passes to op amp A_{6} configured in this phase as an
integrator. The integrator output produces a current energizing LED of the
second, call it LED optocoupler whose photoresistor R_{L1} is
included to the input AC attenuator.The closed control loop automatically varies the attenuation until reaching V _{D} = V_{REF}, the reference being chosen for setting
I_{OUTA} at a level of about 10mA. This level is attainable in the
whole 0,1-1V RMS range of input AC voltages and, as gain of the broadband
amplifier A_{2} is fixed (about 38 with the components shown), the
degree of attenuation might serve a measure of the applied AC input.
Unfortunately, the accuracy of keeping I_{OUTA} isn't very high
because of V_{REF} fluctuations and drift of the converting
optocoupler transfer characteristic with temperature, time and other
factors.To avoid this, the second, DC phase of operation is introduced. During its 0,3s, the state of all the switches is opposed to that of the AC phase, so the optocoupler is supplied by a DC current I _{OUTD}. Here the
second control loop including the same optocoupler, the same V_{REF}
and A_{5}, but also integrator A_{8} and amplifier
A_{4} is closed, and setting I_{OUTD} is carried out
according to the simple relationshipThe main result of the described two-phase operation is equality of the RMS values of the alternating I _{OUTA} and direct I_{OUTD}
currents, its accuracy depending only on the control loops' performance
which is determined by offset voltage and open-loop gain of the op amps
involved.The achieved equality I _{OUTA} = I_{OUTD} doesn't suffer
the above drawbacks of the converting optocoupler and reference
V_{REF} because of the continuous character of switching.Controlling in the two loops is performed in turn, it means that in every moment only one loop is closed. The other must remember its preceding settled state, otherwise their smooth operation will be broken. The open switches S _{3B}, S_{3A} configure in turn A_{6}
and A_{8} as analogue memories. Chosen durations of the operation
phases (0,7s and 0,3s) satisfy a trade-off - they are short enough for
A_{6} and A_{8} to store the settled outputs on
corresponding capacitors without degradation and for the optocoupler and
V_{REF} - not to be subjected to any perceptible drift.At the same time they are long enough for the system to respond to a disturbance, the first phase being longer as the AC loop handles variable AC input voltages, while the DC loop is running practically in the steady-state mode (variations of V _{IND} indicate only to the
above imperfections of the optocoupler and V_{REF}).To produce a DC output which could watch the state of the input attenuator and hence the level of AC input, op amp A _{3} is employed. It
amplifies the applied fraction of DC voltage V_{IND} with the
gain just equal to the AC attenuation because the used resistors
R_{1}, R_{2} are the same. This results in the
DC-component of voltage V_{E} at point E. The AC-component
V_{INA} remains unchanged, as it sees the output of A_{3}
which here behaves itself as a low-pass filter whose cut-off frequency
(8Hz) is determined by R_{6}C_{1}.Pure DC output V _{OUTD} of the converter is obtained after passing
V_{E} through a forth-order Bessel filter (A_{9},
A_{10}) chosen for its optimum settling time. The filter turnover
frequency is 2,4Hz and the AC products are suppressed effectively - about
60dB even at the lowest (20Hz) frequency.Expression for V _{OUTD} isCombining it with the previous formula gives: As I _{OUTA} = I_{OUTD}, their expressions must be equal
too:Exclusion of such a variable term as R _{1} (along with
R_{2}) is of vital importance and leads to:The final simplification comes when choosing R _{02} =
R_{01}, R_{8} = R_{34} and R_{7} =
R_{5} + R_{05}. Slight adjustment of R_{7} allows
to set the desired exact equality of the RMS value of AC input and the
obtained value of DC output:V _{INA} = V_{OUTD}.
ACCURACY Accuracy of maintaining the last equality depends on various factors. However, thanks to the applied circuit tricks, such crucial parts of the converter as its optocouplers have been excluded from the main contributors of measurement errors. Indeed, running the led optocoupler simultaneously and the converting optocoupler quasi simultaneously in two processes, AC and DC, ensures the conversion accuracy not to be affected by kind and stability of their transfer characteristics. This considerably simplifies also the choice of the optocouplers, these devices can be obtained by putting together separate components. The required for that are a pair of cadmium sulfide photoresistors with a minimum cell resistance of not more than 1kΩ and settling time not exceeding 100ms, a miniature 6V/20mA filament lamp and at last a miniature red LED. The only two errors associated with the optocouplers have been encountered. First of them is a slight nonlinearity of photoresistor R _{L1} included in the input attenuator. Increasing R_{L1},
along with rising the AC and DC voltages simultaneously applied to it,
more clearly reveals this effect which is due to the property of the
photoresistor's light sensing material. At the top end of the 0,1-1V RMS
input dynamic range, the nonlinearity error reaches ±0,1%.The second error is caused by AC modulation of photoresistor R _{L2}
used in the converting optocoupler. At low working frequencies, the
thermal inertia of filament lamp L becomes insufficient and a ripple of
the emitted light intensity appears. This results in R_{L1}
modulation and then in the ripple of DC output of the optocoupler, the
ripple frequency and amplitude being correspondingly twice and inversely
proportional to the frequency of AC input V_{INA}. The error
would be ±1% at 20Hz but further I will show how it has been reduced at
least to ±0,2%.The ultimate conversion relationship V _{INA} = V_{OUTD} is
obtained by bringing into proper correlation the values of R_{01},
R_{02}, R_{3}, R_{4}, R_{5}, R_{8}
and by final adjustment of R_{7}. Long-term stability of these
resistors directly determines the conversion accuracy, so to guarantee
the latter not to be affected by time, temperature etc, metal film ±0.5%
resistors should be used. This eliminates the need of any periodic
calibration.Most numerous are the so-called static errors of the RMS converter. The key condition of running the converting optocoupler is equality of its DC output and reference V _{REF}, i.e. V_{D} = V_{REF},
the accuracy of its maintaining depending on such DC characteristics of
the involved op amps A_{4}, A_{5}, A_{6},
A_{8} as offset voltage, bias current and open-loop gain.
Fortunately, V_{REF} =1,5V is high enough to ignore for example
the input offset of A_{5}, which for the used OP07H doesn't exceed
0,1mV, so its trimming is unnecessary.Notably lesser are the DC voltages applied to the inputs of op amp A _{3} and final low-pass filter (A_{9}, A_{10}),
both stages forming the converter's DC output V_{OUTD}. They are
correspondingly 50mV and 0,1-1V, so the input offset of OP07H leads here
to such maximum static errors as ±0,2% and ±0,1%. They further can be
easily reduced to negligible levels by the adjustments provided in
A_{3} and A_{10}.At low working frequencies, the error caused by the residual AC ripple of output V _{OUTD} is added to the above modulation error. The used
smoothing forth-order low-pass filter with its 2,4Hz turnover frequency
allows to retain this error within ±0,2% even at the lowest 20Hz frequency.
At high frequencies, the errors associated with amplifiers A _{1},
A_{2} become dominating and the highest attainable bandwidth limit
may be roughly taken as a frequency at which open-loop gain of amplifier
A_{2} falls to 60-80. Accuracy largely depends also on the
amplifier slew rate and stray capacitances in the whole route of passing
AC signals.The achievements in creating broadband op amps make it possible to widen the converter bandwidth up to 30MHz, but when turning to the discrete technique, a good bit higher figure can be obtained. In the author's prototype, A _{2} is an all-discrete FET input amplifier with an
open-loop gain of 1000 at 1MHz and a slew rate of 300V/µs. The achieved
total accuracy of the RMS converter is better than ±0,3% at frequencies
from 20Hz to 20kHz and ±0,5% - from 20Hz to 100kHz in the whole 0,1-1V RMS
range of AC inputs with up to 10:1 crest factor. The accuracy remains
still high (±1%) at 1MHz, being reduced to ±5% at 10MHz.
CIRCUIT DETAILS As can be seen from the converter’s full circuit diagram (Fig.2), a certain part of circuitry is employed to keep the total settling time within 1,5s in the whole 0,1-1V RMS range of AC inputs. The used diode-resistive networks reduce the integrators’ time constants, speeding up the start of controlling when sharp input disturbances occur. To provide optimum completion of the controlling process for any V _{INA}, the AC control loop contains an automatic attenuator
R_{26}, Q_{12} which reduces excessive gain within the
loop when R_{L1} is high and the current through the LED optocoupler
needs a low output of integrator A_{6}. The less this output and
its fraction applied to op amp A_{7}, the less the on-resistance
of the two matched JFETs biased equally by A_{7}, one of them
(Q_{12}) shunting the integrator input. This damps an oscillation
tending to appear at V_{INA} levels of more than 0,3V RMS and
ensures the controlling process to be fast-settling aperiodic.If during the AC phase of operation considerable changes of the AC input take place, the system must respond to them, not being interrupted by the following DC phase. Forcing flip-flop U _{6A} to stay in the former
state for about 2s is carried out by a high going output pulse of
monostable U_{6B}, the necessary triggering signal for the latter
being derived from the output of A_{5} and then amplified and
formed by Q_{8} and U_{5A}.The two-phase operation is ceased at all when the input AC voltage drops below about 70mV RMS, the integrator A _{6} output reaches a
maximum for the given op-amp level and the system looses its ability to
maintain the current balance in the converting optocoupler. In this case
U_{6A} stops generating and gives at its Q output a steady high
level corresponding to the closed DC control loop and to sending the
direct current I_{OUTD} to the optocoupler. The inhibiting signal
applied at that time to the S input of U_{6A} is obtained via
U_{5B} from a simple comparator on Q_{6} which is on when
the peak-detected AC output becomes less than the set emitter potential.
To avoid incorrect results of conversion in this mode of operation, the
output of Q_{6}, inverted by U_{4C}, enables switch
U_{3C} to shorten the input of A_{4}. This removes the
DC-component of V_{E} and the converter output V_{OUTD}
is turned to zero.The continuous, not affected by any switching AC output V _{OUTA}
is normally about 4V RMS, but its short dropping occurred during abrupt
transitions of the AC input (particularly from maximum to minimum) has no
influence on the generating U_{6A}, as NOR-gate U_{5B}
allows to do that only if the system fails to reach the balance
I_{OUTA} = I_{OUTD}, and the integrator A_{6}
output is therefore maximum.Voltage V _{OUTA} is also applied to an amplifying and clipping
integral long-tail pair Q_{9} -Q_{10} which along with
U_{4D} forms a synchronizing signal for U_{6A}. The
necessity of such synchronization is dictated by the effect of AC
modulation of photoresistor R_{L2}, which is caused by the
alternating nature of the passing through lamp L current I_{OUTA}
and manifests itself largely at the lowest frequencies. As a result, a
certain AC signal is present at the input of integrator A_{6}
and its capturing, done at the moment of completing the AC phase of
operation, leads then to periodic variations of photoresistor
R_{L1} and ultimately to unstable output V_{OUTD}. This
phenomenon is practically eliminated if commencing every phase coincides
with the AC signal zero-crossing, just what the synchronization performs.
The final contribution to the total settling time of the converter is done by the output DC amplifier A _{3} and output filter
(A_{9}, A_{10}). The introduced delays don't exceed
correspondingly 0,7s and 0,5s (for a 0,1% settling accuracy) and,
although overlapping, they are an inevitable payment for the attained
accuracy of conversion at low, down to 20Hz frequencies.ADJUSTMENT Before using exotic broadband amplifiers and driving the RMS converter at radio frequencies, it's reasonable to test and adjust the circuit in the audio range, with the help of for example a widespread OP37 or even TL082 chosen as A _{1}, A_{2}.First the required operational point of the converting optocoupler (a 10mA current through its lamp) should be set, whether it is a ready available device or made from the recommended above separate parts. For that, force the converter to run all the time in its DC mode by seating the disconnected S input of flip-flop U _{6A} to +15V supply via
a 15kΩ resistor. Choose R_{10} to obtain voltage across
R_{02} near to 2V and then check the equality of absolute values
of voltages V_{D} and V_{REF} (at about 1,5V) applied to
summing amplifier A_{5}.To set flip-flop U _{6A} to the steady state corresponding to the
AC mode of operation, ground its S input and seat the disconnected R
input to +15V. Apply a 1kHz 100mV RMS test signal to the converter input
and choose R_{30} to obtain the DC voltage across it within
4,5-5,5V, at the same time the AC signal on R_{01} being near to
2V RMS. Observing this signal on an oscilloscope, make sure that it remains
unchanged after the settling process caused by a 20dB step increase of AC
input V_{INA} (to 1V RMS). If amplitude ringing occurs, damp it
by adjustment of trimmer R_{39} and then observe the reverse
process, when V_{INA} drops to 100mV RMS. Its duration must be
within 0,5s, otherwise continue the optimization.Restore the circuit initial connections and check its two-phase operation, monitoring pulse signals at the outputs of generator U _{6A} when
input V_{INA} is within 0,1-1V RMS. Adjust trimmer R_{51}
to cease the generation when V_{INA} is less than 70mV RMS.
Apply an AC input V_{INA} =1V RMS and set its exact output DC
equivalent V_{OUTD} by adjustment of R_{47}. Reduce
V_{INA} to 100mV RMS and compare it first with the DC component
of voltage V_{E} (at point E) and then - with the converter output
V_{OUTD}. The first difference, if takes place, can be removed by
offset trimming of op amp A_{3}, the second - by offset trimming
of the output filter (A_{10}).Imitating all the possible transitions of AC input, measure the DC output settling time, its value of less than 1,5s confirming the correctly made component choice and circuit adjustment. Finally, the accuracy of maintaining the conversion relationship V _{OUTD} = V_{INA} should be evaluated at several,
particularly near to the ends, points of the input 0,1-1V RMS range and
at the lowest, mid and highest frequencies of the expected bandwidth.To widen the dynamic range of RMS measurements, the converter should be preceded by a broadband amplifier or attenuator. pdf version here HOME full circuit diagram |