Measuring AC

Since the average of a purely sinusoidal waveform is zero, the meter needs to measure either the peak-to-peak voltage, the average rectified voltage or the true RMS voltage. For the same AC signal, the displayed values will be different! For example, if we set up a waveform gener-ator to give a 10V sinusoidal waveform output it will have a peak-to-peak voltage of 10.00V, a rectified average voltage of 6.37V and an RMS voltage of 7.07V. Electronic multimeters use RMS because this is the equivalent DC voltage that would give the same heating effect with a resistive load. However, if the AC signal is not a pure sine wave, the readings will be very different depending on the waveform:



The solution to all of these problems is a “True RMS” multimeter which can accommodate both the AC and DC components of continuous waveforms and display the correct result:



However, the situation is made more complex if the AC signal is discontinuous. Then, even a true RMS voltmeter will not give the current reading. Unfortunately, such discontinuous signals are very common in AC/DC circuits, such as the trapezoidal signal from a switching transistor, the saw tooth voltage across a diode or the triangular voltage across an inductor. The equivalent RMS voltage is an integral over time:



So the only way to measure the RMS value of a discontinuous signal accurately is with an oscilloscope.

With any digital meter or digital storage oscilloscope (DSO), another important source of error is the crest factor. This is simply the ratio of the peak to RMS voltages. If a digital meter is to measure the signal accurately, it must have sufficient dynamic input voltage range to cope with the crest factor which can vary from 1 for a square wave, √2 for a sine wave up to 10 or more for an asymmetrically pulsed input.





Practical Tip: passive oscilloscope probes must always be calibrated before any AC measurements are done. All oscilloscopes have a square wave reference output on the front panel. The oscilloscope probe should be hooked on to this output and the small variable capacitor in the plug adjusted until the display shows a flat-topped square wave. Figure 4 below shows two identical probes connected to the same internal square wave source. Channel 2 is correctly adjusted. Channel 1 is not:



For most measurements, the 10:1 attenuator setting should be used on the probe. This will increase the probe’s DC impedance from 1 MOhm to 10 MOhm and reduce the loading of the probe on the measured signal at the cost of a less accurate measurement of very small signals.

Great care must be taken when measuring high voltages such as AC mains or rectified AC using oscilloscope probes. The ground connection of the probe is connected to earth via the power lead, so simply connecting the probe to the high voltage circuit will blow the fuse or trip the earth leakage detector in the mains supply.

There are several solutions to this problem:

1. use an isolated active probe.
2. use an active differential voltage probe (also isolated, but with a higher input voltage range)
3. run the oscilloscope from a mains isolation transformer and disconnect the ground wire. Also make sure that here are no connectors used for remote control (GPIB or USB) that could ground the oscilloscope through the data lines.

Note that option 3 means that any exposed metalwork (for example the BNC connectors) may no longer be a ground potential, so be especially careful when using an isolated oscilloscope. To measure hazardous voltages, use only option 1 or 2.

Practical Tip:when using an isolated probe or isolated oscilloscope, the probe tip and probe ring can be connected between any two arbitrary points on the circuit being tested. However, the ring should be connected to a stable voltage and not a switching node to avoid false readings. In the following example, the correct way to measure the voltage across a totem pole PFC choke is to use two probes and then use the mathematical function of the oscilloscope to display the difference:



High frequency AC voltage measurements

The 10%-90% rise time of a probe is related to its bandwidth with the formula:



This means that the commonly used 20MHz BW limit setting will stop the oscilloscope from reacting to any edges that are faster than around 17.5 nS. This is great for removing unwanted switching artefacts from low frequency AC/DC converters but not so good for the next generation of fast switching SiC or GaN-based power supplies where such rise times are part of the signal.
The AC impedance of an oscilloscope probe is the summation of the various impedances in series and parallel of its component parts, so the voltage seen by the DSO will be equal to:



These additional impedances will cause an overshoot (ringing) for a step change which can be usually be successfully dampened out by measuring the high frequency signal via a high ohmic series resistor and/or by avoiding the use of the probe ground clip (the clip has the highest impedance of all of the impedance factors).

The following diagrams are reproduced from the DC/DC book of knowledge to show the adverse effect of using the ground clip when measuring ripple and noise:



AC Current Measurement Techniques

Precision Shunt Resistor

If a precision resistor is placed in series in a circuit, the voltage developed across it is directly proportional to the current flowing through it. This is the principle by which most multimeters with a current input measure current. If the meter has a full scale reading of ±200mV, a 100 mOhm shunt resistor will allow up to ±2A to be measured. A very simplified multimeter schematic with selectable full scale voltage and current ranges is shown below:



The 100mOhm shunt resistor must be kept low-ohmic so that the in-circuit voltage drop is insignificant (in the example above only 200mV) and to reduce the errors caused by self-heating. All resistive materials have a temperature coefficient of resistance (TCR) which will cause a change in the resistance with temperature, so it is important that the shunt resistor is made of a material with a very low TCR, ideally less than ±100 ppm/°C.

For a fixed shunt resistor on a PCB that is used to measure direct or alternating currents, the additional errors caused by the copper tracks can become very significant (copper has a typical TCR of around +0.004%/°C or +4000ppm/°C). To avoid measurement errors, four terminal (kelvin contact) shunt resistors should be used, so that the voltage measurement tracks are not carrying any significant current themselves:



The advantage of shunt resistors is that they can be used to measure both DC and AC currents and that they can be suitably dimensioned to measure both very small and very large currents. With careful track layout, shunt resistors can also be used to accurately measure high frequency alternating currents.

Often a simple low pass filter formed by a capacitor in series with the shunt and high ohmic resistors placed in the measurement legs will allow clean current measurements to be made even on noisy installations. Finally, the performance does not deteriorate with short-circuit or high surge currents: there is no avalanche or thermal runaway failure mode.



Practical Tip: current shunts can run hot enough to affect adjacent components, so always leave a good clearance gap and use thick copper traces to help dissipate the heat. High current capability shunts are often raised off from the PCB. This avoids overheating the FR4 material beneath the central high-resistance hot-spot of the shunt and helps with air cooling. Check also that the expansion coefficients of the shunt and PCB are not too mismatched to avoid thermally-induced cracking and solder-joint stress.

The disadvantages of using a shunt resistor are that the measurement contact is direct without any isolation, that the power dissipation in the shunt resistor can affect the readings and that very low ohmic shunts need high voltage magnification to generate a useful signal which introduces noise, drift and offset errors. Furthermore, high precision power shunt resistors (0.1% or better) with low TCR and low drift are expensive components.

Shunt + Current Mirror

As a current sensing shunt resistor is not isolated nor necessarily referenced to ground, this can create problems when attempting to measure the current in a higher voltage circuit. The following example shows how to use a current mirror to voltage shift the current output to a level, say, suitable for the input pin of a microcontroller. DC and DC offset AC (for example output ripple current) can be measured with this circuit.



The voltage developed across the current sense resistor, R_s, is amplified by the Op-amp to generate an output current, I_sense = Rs /R. As this current is referenced to the high voltage supply, it needs to be current mirrored to generate an output voltage, V_sense, which is referenced to the 5V supply.
The V_sense output voltage is:



Shunt + isolation amplifier

The use of a current mirror in combination with a high-side shunt resistor is useful for medium supply voltages, but not safe for higher supply voltages. To measure the current in a PFC stage or AC conductor, safety isolation is required. One technique to accurately measure AC or DC currents on a high voltage supply is to use an isolation op-amp with an isolated DC/DC supply:



Current transformer

A transformer can be used to measure the AC current flowing in a conductor if the conductor passes through it to effectively make a single turn:



The secondary current, I_S, is proportional to the primary current, I_p divided by the secondary turns:



Current transformers (CTs) are useful for measuring high AC currents as the output current can be made a ratio of 20:1 to the conductor current by simply winding 20 turns on the secondary. If more sensitivity is required, then the primary conductor can be wound twice around the core to increase the full scale reading to 10:1. Split-core versions are also available that can be clamped around a conductor or opened to allow more primary turns to be added without needing to cut the wires.

Practical Tip: Never operate a current transformer without a load. If the output current has a 20:1 attenuation, then the open-circuit output voltage has an x20 multiplication, so a current transformer measuring mains current can easily generate thousands of volts across the terminals if the load is disconnected. Always short circuit the outputs if the load is not attached!
Current transformers cannot measure DC currents, so only the AC component (for example, the ripple current) will generate an output signal. As the measurements rely on the performance of the high permeability magnetic core, a current transformer will have a bandwidth limit, a rated minimum and maximum primary current, a maximum primary voltage rating and an accuracy rating (typically between 0.2% and 3%, valid over a primary current in the range of 5% to 120%). Finally, CTs have a maximum output burden rating due to the secondary impedance interacting with the ammeter load. If the output load is too high, the output reading will be too low and the CT will also load the supply.

The main advantages of a current transformer are an output which is also a current source, high isolation withstand voltage, near-lossless measurement and a bidirectional output.



Compensated CT (AC Zero-flux)

To increase a current transformers low-frequency response, a feedback circuit can be added to cancel out the load caused by the secondary winding. A separate winding is used to cancel out the magnetic flux in the core:



AC zero-flux CTs eliminate the B-H characteristics of the magnetic core, so offer high linearity, low insertion impedance and a wide bandwidth. However, the detection winding and AC amplifier add cost.

Rogowski Coil

Although similar in appearance to a split-core current transformer, a Rogowski Coil (RC) does not operate in the same way, generating an output voltage proportional to the measured current instead of an output current. An RC needs no magnetic core which reduces the cost and the loading on the primary conductor and the quick response is useful for measuring small, fast changing currents.



The output voltage v(t) is dependent on the rate of change of the primary current, I_p:



Where A is the cross-sectional area of the core, N the number of secondary turns with length l and μ₀ is the magnetic constant, 4π x 10^-7. As these are all fixed units, the resulting output voltage is simply equal to the rate of change of the primary current dI_p/dt multiplied by –M, a constant dependent on the mechanical dimensions only.

The secondary wiring is wired in a helical arrangement with the return wire passing back under the secondary so that both wire ends are at the same end of the open core. This makes it very useful for clamp-style current meters as no wires bridge the gap. Flexible RC designs exist where the secondary is wound over a plastic tube that can simply be wrapped around the primary conductor or conductors.

As the output is proportional to the rate of change of the primary current rather than its absolute value, the signal is usually integrated with an operational amplifier to generate a voltage that is directly proportional to the current. This introduces some errors in the measurements due to amplifier offsets and integration times and creates a frequency response that drops off at both low and high frequencies. Nevertheless, over a wide range of frequencies the response is linear and flat.

Hall Effect Current Sensor

The Hall Effect current sensor relies on monitoring the voltage induced by a magnetic field created by the primary current rather than measuring the current directly.
When current flows through a thin flat conductor, no potential difference appears across the transverse (longer) sides unless the charge carriers are influenced by an external magnetic field. The magnetic field exerts a transverse force which causes a charge imbalance to occur, resulting in a voltage developing between the transverse sides which is proportional to the magnetic field strength.



The hall voltage, V_H, is directly proportional to the bias current, I, and the magnetic field strength, B, and inversely proportional to the number of charge carriers per unit volume, n, the charge on each carrier, e, and the thickness of the flat conductor, d:



The hall eff ect will occur in any flat conductor, but as n= 10²⁹ m^-3 for copper and n= 10²⁵ m^-3 for silicon, the resulting hall effect voltage for a silicon conductor will be 1000 times greater. Therefore semiconductors are more often used rather than metallic conductors for Hall Effect sensors.

The bias current, I , can be supplied from a constant current source to create an output that is only dependent on the external magnetic field strength, B or the sensor can be placed between the poles of a permanent magnet in order to measure an external bias current. In this way, the hall sensor can measure DC current.

To use a Hall Effect sensor to measure AC current in an external conductor, it can be placed in the air gap of a transformer core through which the primary conductor passes:



Hall Effect current sensors can measure large currents or low currents, depending on how they are set up. Unlike the Rokowski coil and current transformer, a Hall Effect current sensor can be used to measure both AC and DC currents.

However, the performance of the magnetic core, external magnetic fields and amplifier errors such as offsets or gain drift can reduce the measurement accuracy.

Flux Gate current sensor

A flux gate current sensor combines elements of both the Hall Effect and AC zero-flux sensors. The current flow through the primary conductor creates a magnetic field which is detected by a probe coil inside the gap normally occupied by the Hall Effect sensor.



The output is amplified and fed back into a secondary winding to nullify the magnetic field as in the zero-flux sensor. The compensation current can be returned to ground via a resistor to give an output voltage proportional to the current flowing in the primary conductor. This closed loop system creates a more accurate measurement than other equivalent current sensors as temperature and aging effects can be compensated out, it also means that DC currents can be measured.
The magnetic material used has a non-linear B-H characteristic, so it saturates very easily. The Fluxgate controller uses this non linearity to make a very sensitive measurement system, relying on the feedback to bring the magnetic flux back to zero for any small changes in primary current and on core saturation to protect the system from heavy over current situations such as a primary short circuit.



Fluxgate transducers make very good residual current measurement (RCM) sensors. An AC cable carrying both live and neutral wires is placed inside the sensor. The magnetic field from the supply and return conductors cancel out, leaving only any difference to be accurately sensed and amplified.

The disadvantages of the fluxgate current sensor is that any residual core magnetism caused by exposure to external magnetic fields will distort the measurements. Smart fluxgate control-lers have a demagnetisation function to reset the core with a controlled AC drive signal before making a new measurement.

GMR current sensor

Giant Magnetoresistance (GMR) is a quantum spin effect that causes certain layered ferromagnetic materials to change their resistance under the influence of an external magnetic field. The sensor is placed in the gap of a magnetic core in the same way as the Hall Effect current sensor to measure AC current or placed in a coil to measure DC current.

A GMR sensor consists of a Wheatstone bridge with two active GMR elements and two passive shielded legs. This doubles the output sensitivity to the ΔR change to the intrinsic resistance, R, caused by the GMR effect.



The GMR sensor has a very fast reaction time and is very sensitive, so it a useful sensor for measuring small signal AC currents up to 5MHz. Despite the Wheatstone bridge arrangement, it still needs careful thermal compensation for accurate readings as the GMR effect is relatively weak.