Meters, Power Supplies and Generators

1. Meters

Generally analog meters respond to the average of the signal being measured. This is due to

the mechanical mass of the pointer and the RC response time of the electronics. Since the

average of most ac signals is zero, ac meters require more circuitry to measure values of time

varying voltages. Many meters can function as both current and voltage meters. Usually there

are separate inputs for the voltage and current functions. Trying to use the instrument as a

voltmeter, when the leads are connected to the current input will either destroy the meter or

blow a fuse.

Voltage Measurements Voltage is analogous to pressure in a water pipe. And like pressure, it has to be measured

relative to a reference. A voltage is measured across a circuit component, to indicate the

voltage difference or voltage “drop”.

The dashed lines in figure 1 indicate that all parts are contained within one physical unit. In this

case, the resistance is a part of the meter and there is no way to separate it from the meter. An

ideal voltmeter has a resistance of ∞Ω.

Figure 1: The Voltmeter

To measure voltage electronically, a voltmeter uses a known, stable, resistor. All voltage

meters draw current, because of that resistor. A typical digital volt meter (DVM) has a

resistance of 10 MΩ while some older analog meters may be as low as 3.2 kΩ.

Current Measurements Current is the rate change of charge and is, therefore, a measure of the number of electrons per

second moving through a circuit. Since the current into and the current out of a lumped

component are equal, you cannot measure a current “drop” across a component. To measure

current you have to measure the actual charge flow through the wire.

This measurement is done by inserting relatively small resistor in series with the circuit and

measuring the voltage drop across the resistor. This is normally shown transformed into a

series resistor and an ideal (resistance of 0Ω) current meter. The series model is shown in

figure 2. In the typical digital multimeter (DMM), on a 2A range, the resistance is 100 mΩ.

Because a current meter has resistance, it will cause a voltage drop and may affect the operation

of the circuit. The actual amount of resistance depends upon the sensitivity of the meter. For

example, the DMM on a 200 uA range has a resistance of 1 kΩ, while a nanoampere meter will

be more than 100 kΩ.

Figure 2: The Ammeter

Resistance Measurements

An ohmmeter applies Ohm’s Law to determine resistance. Ohm’s Law states the voltage =

resistance x current. By applying a known voltage (produced by an internal battery or

transformer) to a resistor and measuring the current flow, the resistance can be determined.

Power Measurements A wattmeter measures the product of voltage and current to determine the power in watts.

Measurement Errors This is a complex issue and we will only cover the basics. An error causes the measured value

to be different from the actual value. Human, or gross, errors are usually due to mistakes in

using or reading an instrument. Two examples are viewing an analog meter needle at an angle

rather than straight on (parallax error), and

reading the wrong meter scale. Other errors

may be caused by the instruments themselves.

Plots of data (figure 3) typically include error

bars, which indicate the accuracy of the

measurement, the effect of the meter loading

upon the circuit, etc. Plots of theoretical

calculations can also include a tolerance to

account for the non-perfect circuit components

(ie ±1%, ±5%, etc), temperature variations, etc.

Figure 3: A Plot Illustrating Error Bars

Accuracy The accuracy of a measurement is how close the value came to the actual value that exists, not

the theoretical one. Instrument accuracy is usually broken down into systematic errors and

random errors. The systematic errors are either instrument related (ie friction in a mechanical

meter pointer bearing) or environmental. The method by which the meter works (mechanical,

electrical, ..), and the “quality” of design and construction, greatly affect how large these errors

are. Quite often both of these are further broken down into static and dynamic errors. Dynamic

errors would be caused by the meter not being able to respond fast enough.

Precision Precision pertains to the number of significant figures and the repeatability of a measurement.

High precision instruments provide more significant figures and have greater repeatability.

Resolution This is the smallest change in the quantity being measured that an instrument will indicate. For

a digital meter, this is simply one of the smallest digits. With an analog meter, this is usually ½

of the smallest divisions on the meter face.

Repeatability The repeatability is a measure of the fluctuations which are due to noise and errors that are not

repeatable. When a measurement is repeated several times, and then statistically analysed, the

repeatability can be expressed as the standard deviation.

Uncertainty This is the combined effect of accuracy, precision, repeatability, noise, and errors on the

measurement. It represents how uncertain the measurement is.

1.1 Calculating Meter Error

Digital Multimeters The DMM is the most common instrument you will encounter. The precision of a DMM is

usually expressed in digits. The most common model has 3 ½ digits. That means that you

have three “full” digits that are capable of indicating from 0 to 9 and one ½ digit. The ½ means

that a +1, blank ie. 0, or -1 can be displayed. There are also 4 ½ and 5 ½ digit meters as well as

3/4 digit meters. A 3/4 digit meter can display +2, +1, blank (0), -1 or -2 as the leading digit.

A DMM has two sources of systematic error. One part of the error is due to tolerances in

resistors. It is expressed as a percentage of the input and therefore varies with the magnitude of

the voltage being measured. The second part of the error is due to the digital conversion

process. It is fixed for a given meter range and is expressed in the number of “digits” to which

the reading is accurate. Each “digit”, has the value of a single count of the right-most digit on

the display.

For example, consider a reading of 1.345V on a 2 V dc range. The meter displays a maximum

of 1.999 V on this range. The smallest change on the meter display is 0.001 V.

Then the errors are,

percent error: 0.1% * 1.345 V = 1.345 mV

digit error: + 1 digit = 1 * 0.001 V = 1 mV.

Therefore, V = 1.345 V ±2.345 mV or V = 1.345 V ±0.17%.

Now consider the same measurement on the 20 V range. The reading would have been 1.34 V

and,

percent error: 0.1% * 1.34 V = 1.34 mV

digit error: + 1 digit = 1 * 0.01 V = 10 mV.

Therefore, V = 1.34 V ±11.34 mV or V = 1.34 V ± 0.85%.

This shows that the most accurate measurements are made on the lowest meter range that will

accommodate the measured value.

If the meter were to read 16.32 V (rms) while measuring an 8 kHz triangle wave on a 20.00 V

RMS scale; how large is the error? The meter measures True RMS and we can trust a reading

done on a triangular wave. On the AC range the error is 0.5% + 2 digits. Then the errors are,

percent error: 0.5% * 16.32 V = 80.6 mV (rms)

digit error: + 2 digits = 2 * 10 mV = 20 mV (rms)

Therefore V = 16.32 VRMS ± 101 mVRMS or V = 16.32 VRMS ± 0.62%.

1.2 Agilent U3401A 4 1/2 Digit Dual Display Multimeter

The Agilent U3401A in the lab is shown in 4 and its front panel controls are described below. Agilent

U3401A is a 4 1/2 Digit Multimeter.

DMM Range

• The range is not explicitly indicated on the screen.

• You can adjust the range of DMM1 by noticing:

– The number of the displayed digits after the decimal points,

– The measurement unit displayed on the screen of DMM1, and

– The set of possible ranges for the voltages and currents which can be found in the tables

in the Appendix.

Figure 4: Agilent U3401A Front Panel

1.2 Meter Loading

Every meter affects the circuit it is connected to by drawing current (voltmeter) or adding a voltage drop

(ammeter).

Analog Meters

An analog voltmeter’s resistance is usually specified as a sensitivity in ohms/volt. For example, the

sensitivity of the Simpson analog voltmeter (Model 260) is 20 kΩ/volt. The resistance for a particular

voltage range is determined by multiplying the sensitivity by the full scale voltage on that range. As long

as the voltmeter draws much less current than the component across which it is connected, we can

say that its effect will be small.

Ammeters are more complex. The standard shunt resistance in an ammeter (precision resistor in the

meter) has a 50 mV drop at the maximum current rating. Since this voltage is usually small, an ammeter

should not affect the circuit too much. Remember that every time you change the range, the shunt

resistance changes. Since the shunt resistance, in a normal meter, can vary from milliohms to kilo-ohms,

using the wrong current range can easily affect your circuit.

Digital Meters

For all AC and DC voltage ranges, the DMM has a fixed input resistance which is typically 10MΩ. For

current measurements, the meter will usually have a 200 mV drop at the maximum current, but the

resistance is different for each range. Digital meters are usually more accurate, since they remove

parallax and other mechanical errors. However, if you do not know how to select the range properly, you

can easily get large measurement error comparable to that of an analog meter. The Tektronix DMM4020

used in the lab is shown in Figure 4 and its front panel controls are described below.

2. DC Power Supplies

Adjustable supplies have a control for changing the DC output voltage. DC supplies have two output

leads where one is indicated as being positive (with respect to the other output). Many supplies also

have current limiting. This feature decreases the voltage when the drawn current is beyond a certain

limit. Because of this, the power supply will act as a voltage source until the current limit is exceeded.

Then, it acts as a current source with DC output current fixed at the current limit. In the case of the

Anatek supply, the current limit can be set by the user using a control on the front panel. This control

should be set before you perform any lab experiments. Most components will not explode, or be

destroyed, with 100 mA. If you short circuit the Anatek power supply you will see the current meter

indicate the present current limit. At anytime during the lab, a glance at the power supplies’ current

meter will tell you if you have a short circuit.

Warning: Only perform this short-circuit test on power supplies which have current limiting. If

the power supply is not limited you may start a fire or trigger an explosion.

Power Supply Connections

Most power supplies are “floating”, which means that neither the positive nor negative outputs are

connected to ground or any common point. The Agilent U8001A DC Power Supply used in the lab is

shown in Figure 5 and its front panel controls are described below.

Figure 5: Power Supply Front Panel

3. Signal Generators

A signal generator provides a time-varying signal to test circuits. This can be anything from a simple

sine, square, or triangular wave up to a TV station signal with different types of noise added. The symbol

and basic circuit model for a single-ended (notice the grounded output) signal generator is shown in

Figure 6.

Figure 6: Signal Generator

ROUT is the “output” resistance and may sometimes be called RINT or “internal” resistance. Signal

generators typically have output resistance of 600Ω, 75Ω, or 50Ω. Whenever you draw current from a

signal generator, the voltage at the output terminals will change due to the voltage drop across the internal

resistance. Each generator has an amplitude and frequency control. The controls generally work in

ranges, and you will usually see a range control that limits the minimum and maximum frequency or

voltage and a fine control to adjust within the range.

Function Generators

A function generator is a signal generator that is capable of producing more than one waveform shape.

The Agilent 33220A function generator, shown in Figure , has 50Ω output impedance. Figure is labeled

to indicate the control panel functions.

Figure 7: Agilent 33220

Bottom-Right Button Trigger (9). It is use to enable the sync port, which is a feature used in conjunction with

another equipment (e.g. an oscilloscope).

Output Button (10). Turns on the output voltage, which should be off when the function

generator is initially turned on

Middle Buttons (8)

These six buttons set the shape of the output waveform:

Sinusoidal: A sine or cosine wave; eigenfunctions of LTI systems.

Square: Periodically switches between two values.

Ramp: Also known as a “Sawtooth” wave.

Pulse: A voltage pulse is sent periodically. The pulse width can be tuned separately from the

period (the time interval between repeated pulses). The peak value of the pulse can also be set.

Noise: Simulation of voltage noise.

Arb: Create your own waveform.

Upper-Middle Blue Buttons (7)

These six buttons allow you to select parameters of the output waveform. After selecting a

parameter, the parameter value can be adjusted with the numbered keys, arrow buttons, and the

knob located in the upperright corner of the front panel. Depending on the middle button selected,

not all of these six upper-middle buttons will be active (i.e. not every waveform will require the

use of all six buttons).

Each upper-middle button has two labels above it, with only one of the two labels lit at

any given time. The highlighted label corresponds to the parameter that is currently selected, and

its value will be shown on the display. You will only need to adjust the Freq, Ampl, Offset,

Width, and/or Duty Cycle parameters. If HiLevel and LoLevel are lit, press the button below

LoLevel or HiLevel until Ampl and Offset are selected instead.

Here is a list of the parameter labels and their respective meanings:

Freq: Frequency in repetitions per second. In the case of a pulse, this parameter corresponds to

the frequency at which repeated pulses are sent.

Ampl: Amplitude (peak-to-peak), defined as the distance between the highest and lowest

voltage points of a waveform.

Offset: DC voltage offset. The time-varying waveform is offseted (“raised”) by the constant

offset component (e.g. if you want a sinusoid of amplitude 1 V centered at 3 V, the offset

should be 3 V).

Width: Pulse width (for the pulse waveform).

Duty Cycle: duration of a pulse.

As a reminder, for some waveforms, not all of the parameters are needed. For example, a

sinusoidal waveform only has Freq, Ampl, and Offset available for adjustment.

Upper-Right Buttons (11&12)

In the upper-right corner of the front panel, there is a knob, two arrow buttons, and a set of

numbered buttons. Each of these offers a different way of adjusting the displayed parameter

value:

Knob: This can be turned clockwise and counterclockwise to adjust the displayed parameter

value.

Note that the knob only changes the digit (or number) selected by the blinking cursor.

Arrow Buttons: Press the left and right arrow buttons to manually move the blinking cursor.

Numbered Buttons: An alternative to the knob and arrow buttons is the set of numbered keys.

Simply punch in the desired value using the numbered key pad, and when prompted, select the

proper order of magnitude. Note that the polarity of the output can be changed with the +/− button

Appendix A

Accuracy of the Agilent Digital Multimeter U3401A

Appendix B Agilent 8001A DC Power Supply