Write your name, section, and today's date in the cell below:¶

Name - Section - Date -

Synopsis¶

To learn:
Instruments that measure current and voltage, static or changing with time, and magnetic field,
The influence of an instrument on the measured value.
To do:
Learn how to use a digital multimeter and an oscilloscope,
Learn how to map a magnetic field of a solenoid (optional).

Purpose of this lab:¶

This is the second part of the instrument training and the focus is on electrical signals.
Almost all sensors conducting measurements transform the measured quantity (example: temperature, light, position, time duration, magnetic field, etc) to an electric signal (usually charge or current) that is amplified and changed to a voltage signal. This signal is recorded and displayed by a multimeter, an oscilloscope, or a DAQ (data acquisition) electronics system. It is important to have some basic knowledge about these instruments.

Digital Multimeter¶

The basic function of a multimeter is to measure voltage, current (constant, and the RMS or root-mean-square, or effective values of 50 or 60 Hz AC), and resistance (through Ohm’s Law). Additional functions can include measurements of capacitance, temperature, frequency, silicon diode and transistor, and so on. When the measured quantity is converted and displayed as digital, this multimeter is called a digital multimeter or a DMM. Nowadays the needle based analog multimeter is not commonly used.

Voltage and current:¶

1) One connects the DMM in parallel to the two points when the voltage between them is to be measured. The input impedance of a voltmeter is large (above 1 M $\Omega$ , some around 10 M $\Omega$ ). 2) One connects the DMM in series, in the channel, to measure the current in it. The input impedance of a current-meter or ammeter is small (this is more complicated as a small shunt resistance is needed in the measurement. In this lab we can consider it to be negligible). 3) When the voltage or current is AC, a DMM can only measure the RMS value when the frequency of the AC signal is 50 Hz or 60 Hz.

Resistance:¶

1) Ohm’s Law is used when a DMM measures resistance. A small voltage is applied to the resistor or circuit under measurement. Although this voltage is very small (about 1 Volt or even below), one needs to check to ensure that it does not damage the circuit under measurement when it is very sensitive to voltage.

Oscilloscope¶

An oscilloscope measures voltage as a function of time. As in the case of DMM, and many other instruments, an analog oscilloscope is obsolete. A digital oscilloscope is actually a DAQ system, as the measured voltage is digitized before it is displayed. One can access this data ( $V_i$ , $t_i$ ) for further processing. The math function of the oscilloscope provides common processing such as transforming the signals from the time-domain to a frequency-domain, the Fourier transforms.
An important concept in the measurement with oscilloscope is trigger. One needs to set a threshold on the signal to be measured. Below the threshold it is considered noise. The triggering scheme can be a voltage on the rising or falling edge, or other more sophisticated signal pattern (like pulse width) should your scope trigger offer that. One can also set the scope to “auto”, meaning it will perform the measurement as fast as possible, without a trigger.
The duty-cycle of a scope is very low, usually in kHz range. This means that the scope has a deadtime of about hundreds of microseconds after it triggers on an event. This is much like the point-and-shoot camera. You will not be able to take a second shot immediately after a picture as the camera needs time to read the image from the sensor and store it to the storage card. It is important to remember this long deadtime when one uses the scope to catch a special event (a smart trigger will need to be defined) or to function as a DAQ to record data (only a fraction of the whole data set will be recorded when time between events falls into the deadtime).
The input impedance of a scope is usually 1 M $\Omega$ . In high-end scopes with very wide input analog bandwidth (this means that the scope can see signals with a wide frequency range without distorting them), one finds an internal switch to a 50 $\Omega$ impedance. If this option is not available, one can use a BNC-T connector to terminate the cable to the scope with a 50 $\Omega$ add-on or terminator. This is covered in more detail on a lab focused on signal transmission. The input coupling to a scope can be AC or DC. One chooses AC to block out the DC component in a signal when only the AC signal is of interest. Besides DC, there is also a low frequency cutout when AC coupling is chosen.

Measuring Magnetic Field¶

Hall sensors are commonly used to sense or measure magnetic field. For example, Hall sensors are used to count rotations (rpm, revolutions per minute) of electric motors. This is especially important in brushless (electrically commutated) motors to generate the feedback signal for the controller. A calibrated Hall sensor with a readout unit can be used to quantify the magnetic field where the sensor is placed.
You should have encountered Hall sensora in your introductory electromagnetism class. You can review the basic principles here.

Computer Controlled Instrument and DAQ¶

Modern instruments often have interface to a computer for control and data taking. The commonly used interface protocols are RS232, USB, GPIO (general purpose input and output) and GPIB (general purpose interface bus). An internet search will lead you to the definitions of these standards.
On the computer side, a software will be needed to talk to the instruments. A widely used software is LabVIEW by NI (National Instruments). High level languages from C to Java to Python all have interface packages in them that one can build the control software. Instrument manufacturers often provide such software packages to use with their instruments.

Apparatus¶

Digital Multimeter

Figure 1: Digital Multimeter.

A photo of a DMM which provides the following measurements: - DC or AC voltage and current. - Resistance. - Temperature. - Diode. - Battery under a load. Please note that for current up to 10 A, the plug is different from the one for “V, $\Omega$ , mA, and Temp”, due to the high current values. Other DMMs may have different or more functions, but the basic ones are for voltage, current and resistance.

Function Generator

Figure 2: Signal or Function Generator.

A function generator can produce sine, square and saw-tooth signals with a ranges of frequencies (pattern repeating). One can also change the duty-cycle, DC offset level, or select IEEE standard signal levels. Like DMM and any other instrument, different function generators may have different emphases. Some focus on very pure sine wave generation, others may produce arbitrary waveforms according to downloaded code.

Oscilloscope

Figure 3: Oscilloscope.

This is a two-channel oscilloscope with an external trigger input (like a 3^rd channel without display). Two- or four-channel scopes are common. All channels share the horizontal axis for time. Each channel can be selected as trigger signal. The scales of the vertical and horizontal axis are adjustable within limits of sensitivity and dynamic range. The two parameters that you need to pay attention to when choosing a scope are the input analog bandwidth and signal sampling rate.

Input analog bandwidth determines how fast a signal the scope can measure, before the measured waveform is deformed too much by the instrument’s frequency response. A rule of thumb is that the scope bandwidth needs to be 5 times the highest frequency component (reminder: a square wave has many frequency components) of the measured signal. If you do not care that much of the accuracy of the signal’s rise time, you can reduce that 5 times requirement to 2 times, or use the formula: bandwidth = 0.35/(rise time). Sampling rate indicates the number of digitized points in a unit time. Sampling rate needs to be sufficient for the waveform to be recorded. If you have sufficient sampling rate but insufficient bandwidth, the waveform will be recorded but deformed, or your measurement will have a large error. If the sampling rate is not sufficient, you will not see the waveform, or at least miss many details.

Procedure¶

Using a Digital Multimeter¶

Use the DMM to measure the terminal voltage of the dry-cell batteries and tabulate the battery type, nominal and measured voltages. Make sure that you select the proper measurement range of the DMM. Record your results in the cell below.

Record your measurements here:¶

Battery type - Nominal voltage - Measured voltage -

...

Use the DMM, breadboard and resistors, design your measurement to find out the internal resistance of a 9V battery. Provide a brief description of your setup and record your measurement of the internal resistance in the cell below.

Describe your setup and record your measurement here.¶

Make sure the probe handle is not damaged (the insulation is intact), set the dial to 600V AC and use the DMM to measure the line voltage of a wall outlet. Then set the dial to 200V AC, repeat the measurement. Check your results against US household powering standard.

Record your measurements here, and comment on how it compares to the US standard¶

Use the function generator to generate a sine wave with DC offset set at 0V. Set the amplitude to 3.4V peak-to-peak and the frequency of 60 Hz. You will need a scope to verify the signal generated. Then use the DMM to read the average AC voltage, what do you get? Explain the relationship between what you measure using the scope and the DMM. Now increase the frequency to 600 Hz, 6 kHz and 6 MHz, and repeat the measurement using the DMM. What you get now and why? Provide your measurements and answers in the cell below.

Record your measurements and responses here.¶

Using an Oscilloscope¶

Record the signal (type, amplitude and frequency) the scope signal generator provides. Turn on the measurement function to check if the readings agree with your measurement on the screen (amplitude and frequency). Capture a picture of the screen and paste it in the cell below.

(Technical notes: The cell where you paste your image needs to be a 'Markdown' cell in order to copy and paste the image in, and the file needs to be a png or jpg. Double-click on the cell to modify it. Ensure that your image file is not too large; use an online tool like https://compressor.io/, https://compressjpeg.com/, or https://tinypng.com/ if you need to compress your image file.)

Record your measurements and responses here.¶

Paste your image here¶

Set the trigger at rising and falling edge of the signal, and observe the triggering position in time. Move the trigger level up or down to be in- and outside of the signal level range, and use the running mode of “auto, triggered and single” to see what you get from the scope. You use the provided probe of the scope. What type of probe do you have?

Record your measurements and responses here.¶

Connect the function generator to the scope using a BNC cable. Record the cable type. In the following measurement, use 1 M $\Omega$ and 50 $\Omega$ scope input impedance. Observe the measurement difference.

Record your measurements and responses here.¶

Set the function generator to produce square, sine and tringle waves at 1 V peak-to-peak, 0 DC offset, and at frequencies of 100 HZ, 10 KHz, 1 MHz, 10 MHz and 15 MHz, use the scope to measure the amplitude, rise and fall time (you may search the internet to find the definition, and state the ones that you use in your measurements). In these measurements, you may choose AC or DC coupling at the scope input. Do you see a difference in the measurement?

Record your measurements and responses here.¶

Now set the DC offset to be 0.5 V, use the scope to observe what this means. Do you use AC or DC coupling now? Set the DC offset to -0.5 V and repeat the observation.

Record your measurements and responses here.¶

In the case of a square wave, change the duty-cycle away from 50%, to be 30%, 40%, 60% and 70%, observe the wave form of one full period at frequencies of 10 KHz, 1 MHz and 15 MHz.

Record your measurements and responses here.¶

Go back to 1 MHz, 0 DC offset, 1 V peak-to-peak sine wave, use the math function of the scope and produce the frequency spectrum of the measured waveforms, and compare what you see in the frequency domain with that in the time domain. Now repeat this with a square wave form at 50% duty-cycle.

Record your measurements and responses here.¶

Mapping the Magnetic Field from a Solenoid (Optional)¶

For this measurement, we have only one solenoid and Gauss meter. Groups will need to take turns to do the measurement.

Use the DMM to measure the resistance of the solenoid to decide the voltage to apply to it in such a way that 1.0 A current flows through it. Then use the power supply to apply the chosen voltage to the solenoid. Calculate the magnetic field at the inner center of the solenoid. Use the Gauss meter to measure the field strength at the inner center and ends of the solenoid, and compare with the calculation. You can try a few other locations to get an idea how the field maps out.

Record your measurements and responses here.¶