1. First Year Lab Introductory Electronics We are Physicists. Why do electronics? You will probably also end up using computers! You may end up using optics too. A small atomic physics experiment here (015 Blackett)

2. First Year Lab Introductory Electronics Aims - to introduce… –The equipment –Good lab book keeping –An awareness of measurement and errors –A bit of physics/electronics! Remember… –To use the demonstrators –To colour code your circuits –Be adventurous and inquisitive with your experimentation –Instructions to do something are given in red

3. Equipment Benchtop Power Supply – Gives DC power Digital Multimeter – Measures AC/DC voltage levels, resistance Function Generator – makes sine, square, triangle oscillating waveforms. Oscilloscope Breadboard Wire clippers Resistors/Capacitors/Wire/Banana-banana wires Headphones BNC-banana cables (co-axial, two wires in one cable, a sheath which is usually grounded and a core). Conductors Insulators BNC cable Cross-section

4. Benchtop power supply Meter –Displays output voltage or current Buttons: –On/off –Range - 30V/15V –Meter - amps/volts Knobs –Coarse and fine voltage adjustment Connectors –+V –-V –Ground !??

5. TTi Power Supply On

6. Digital multimeter Buttons –On/off –Measurement type Current Voltage Resistance –Measurement range Connectors –Common –Volts/ohms –Current High (<20A) Low (<2A) Accuracy depends on: –Range (see manual) –How recently it was calibrated Assume 0.5% + 1 digits –1.000 reading has error ± 0.006

7. Use your digital multimeter to meaure the voltage on your benchtop power supply Set power supply to give 10V output Set multimeter to “DC V” & “20V” range Connect using banana leads Do the digital and analog meters agree? How accurate is each meter?

8. Measuring resistance Choose one of the resistors in your component box Attach banana leads to the common and V/  terminals of your DMM and switch to  mode Attach your resistor between the other end of the leads using 2 croc clips Is your resistor within the stated tolerance? Resistor colour code a b c d a.1st digit b.2nd digit c.Power of 10 d.Tolerance (accuracy) 0.Black 1.Brown 2.Red 3.Orange 4.Yellow 10% Silver 5.Green 6.Blue 7.Violet 8.Grey 9.White 5% Gold 47k  ±10%

9. Verifying Ohms Law: V=IR Need to measure the current I through a resistor R when a voltage V is placed across its terminals. Needs 2 DMMs!? Some issues? –Current through the voltmeter? –Voltage across the ammeter? Fortunately, not a significant problem with digital multimeters! Power supply R + A V I V On 20V/20mA range: Ammeter looks like 10  Voltmeter looks like 10M 

10. When circuits get more complicated a breadboard can make life much easier Rows and columns of holes on the breadboard are electrically connected Use your multimeter in resistance mode to check exactly how… Make simple probes: –Banana lead + croc clip –Short length of single strand wire

11. Checking Ohm’s Law - building a circuit on breadboard Power supply R + V A

12. Checking Ohm’s law - what you should have in your lab book A circuit diagram Switch meter from “DC V” to “DC A” to measure current I and voltage V for your different resistors Record values in a table - include estimates of errors Calculate resistance from measured I and V (including the error) Compare to multimeter measured value of R meas I (/mA)V (/V) R=V/I (/  )R meas (/  ) 27.1±0.214.78±0.08545±5548±4 ………… …………

13. Function or signal generator Frequency range (buttons) and value (dial) Signal shape Signal amplitude Outputs V out Com/0V (Ground) Trigger DC offset On/off switch!

14. Function generator + headphones Set the generator to give a 1kHz, 4V p-p sine wave. Connect your 3.5mm jack socket to the function generator terminals and plug in the headphones What does it sound like? –Over what range of frequencies can you hear signals? –Middle C is 262 Hz, what do 131, 524 and 1048 Hz sound like? An octave in musical terms is a doubling in frequency –How does the volume change when you change the voltage range Music is logarithmic! –Set the generator to give square and triangle waves Square and triangle waves contain higher harmonics (multiples of the fundamental frequency)

15. Measuring voltage as a function of time The Oscilloscope: Far too many buttons! Think of groups (horizontal, vertical) Horizontal = time Vertical = voltage (2 identical channels) Channel 1 (vert) Channel 2 (vert) Time (horizontal)

16. Oscilloscope Basics e - beam in evacuated tube. dc voltages applied to X and Y plates deflect e -. Apply sawtooth voltage in time to X- plates (timebase) Apply voltage you want to monitor to Y-plates Y plates X plates Phosphor screen Electron gun t VxVx

17. Exploring (some of) the Controls Turn on `scope, Set CAL knobs fully clockwise Set sig. gen. to 4V p-p, 1kHz sinusoidal. Set ‘trigger’ control to ~ (line) Check ‘coupling’ is DC, not ground Plug sig. gen. into channel 1 of 'scope (use banana-BNC cable) Y-sensitivity knob – multi position rotary –Sets ‘volts per division’ vertically, 1div=1cm. Set to 1V/div Time base knob – multi position rotary –Sets period of saw-tooth, ‘seconds per div’ horizontally. Set to 0.2ms/div If you see a mess DON’T PANIC –Change ‘trigger’ control to AC 2 V/V t/ms t VxVx Screenshot

18. Trigger to the rescue! Input voltage compared with an internally set level – the trigger level After a single sweep of the screen the e - gun waits When the input equals the trigger level the next tooth of the sawtooth is executed t VxVx wait Reference voltage source internal to ‘scope, set by knob on front panel – ‘Trigger Level’ Comparator – gives out pulse when inputs are equal Input voltage Go signal to timebase

19. Trigger explained Sinusoidally oscillating voltage 4V p-p For a trigger level at 1.6V, say As soon as signal goes above 1.6 V the sawtooth triggers At end of sawtooth, `scope waits for next trigger event Play with the trigger level and see what effect it has on the leading edge of the waveform –You may need to press the AT/Norm button Check to see what the +/- or ‘slope’ button does 10 ms/div 0.5 V/div Screenshot 2 V/V t/ms 1.6 25 Trigger point Edge of screen for chosen timebase Trigger point Wait time

20. Trigger Source Can trigger off the signal applied to the channel Or can trigger off a separate signal – external trigger –e.g. a sig. gen. may simultaneously give out a TTL (square) pulse train and a sinusoid. Use the TTL pulse as an external trigger Or can trigger from the mains frequency (‘line’ trigger). Useful for seeing if a ‘noise signal’ is correlated with mains frequency. Plug a BNC-banana connector into the ‘scope Trigger the ‘scope from line Hold the positive banana connector between your fingers Wave your free hand near a mains plug socket Sketch what you see in your lab book. Explanation?

21. Other Notes Cal – ‘Calibrated’ –Change from the calibrated position to make arbitrary sized wave ‘fit’ between grid lines to aid measurement Input Coupling –Ground – shorts scope input to ground – kills signal, allows you to find 0V and set using Vert Position –DC – the ‘normal’ mode, what you see is what you got –AC – removes any DC component of a signal, useful for seeing a small oscillating voltage on a big DC background

22. Plugging your headphones back in… Connect up your ‘scope to the signal generator and plug your headphones back in What has happened to the signal voltage!!? Look carefully at the small print on the signal generator… Connect the headphone jack to the multimeter and measure the headphone resistance … If you don’t measure about 16  then you aren’t measuring the right thing!

23. Potential Divider Two resistors in series form a potential divider V o =I(R o +R L ) giving I=V o /(R o +R L ) I is the same through both resistors so V L =IR L Hence V L =V o R L /(R o +R L ) Calculate V L given your: –Measured headphone resistance, R L –Measured open circuit output voltage, V o –Stated output resistant, R o Are your measured and calculated V L values consistent? Is this true at all frequencies? VoVo ~ RoRo RLRL VLVL Signal generator Head- phones I

24. Oscilloscope input impedance? Look at the small print on the input terminals to the oscilloscope… To calculate the error in measuring a nominal 1V output from the signal generator. V scope =V sig  1M  /(1M  +600  )=0.9994  V sig <0.1% - not really visible on the oscilloscope screen But what is the 25pF all about? –Input capacitance!

25. The effect of capacitance on signals? Unplug the headphones. Set the signal generator to give a 4V p-p 1MHz square wave What do you see on the oscilloscope? –Adjust your oscilloscope suitably and make a sketch in your lab- book

26. Capacitance Throw switch, current flows, plates charge up. Current limited by R. Charged plates set up a voltage that opposes V 0, the current reduces. You have ‘charged up’ the capacitor and the current stops VcVc V0V0 + - R t I V 0 /R 0 t VCVC V0V0 0 I

27. Function generator + Oscilloscope 22pF V0V0 ~ 600  1M  Function generator Oscilloscope Charging Disharging

28. Time Constant V C  (1- e -t/RC ) or e -t/RC Capacitor charges up or discharges exponentially. The time constant RC gives a measure of how long it takes to charge up or discharge the capacitor t=RC t VCVC V0V0 (1-1/e)=63% 0 t=RC t VCVC V0V0 1/e=37% 0 Charging Discharging

29. Square wave into RC circuit Set up the circuit shown on your breadboard using a 1  F capacitor Set the function generator to give a 4V p-p 100Hz square- wave output and observe V out with the oscilloscope Measure the time constant t=RC for your circuit –“Half-life”=0.69  RC CVCVC V0V0 ~ 600  Function generator Estimate the true value of C (remember to include an estimate of your measurement error) Is C within tolerance (-20% to +50%)!! VRVR

30. Impedance - resistance and reactance Impedance describes how an electronic device impedes the flow of current in response to an applied voltage For a resistor the impedance is simply its resistance=R But a capacitor can also impede the flow of current - its impedance is thought of in terms of reactance=1/(2  fC) –Actually it has an effect on the phase of signals too which you will meet later in terms of complex numbers and complex impedances! A capacitor impedes lower frequencies more than higher ones

31. Frequency Dependent Voltage Dividers - Filters A capacitor and a resistor in series makes a frequency dependant potential divider or filter This low pass filter is characterised by its cut off frequency f 3dB –When reactance of capacitor = resistance of resistor –f 3dB = 1/(2  RC) –At f 3dB : V out =V in /  2 Input and output signals are 45° out of phase Can do high pass filter by swapping R and C log[f] 0 V in V out Low-pass filter log[V out /V in ] f 3dB =1/(2  RC) High-pass filter C R C R Why 3dB ? 20 log 10 [  2]=3.0103 decibels

32. Investigating filter performance Switch your function generator to give a sine wave output Using the oscilloscope investigate the way the voltage across the capacitor varies with frequency Measure f 3db and hence get a new estimate for the value of the capacitor CV out V ~ 600  Function generator Is this new estimate for C better than that from measuring the time constant? Could you do better by using the multimeter in “AC V” mode to get a more accurate result?

33. “Listening” to filter performance C V ~ 600  High pass filter C V ~ 600  Low pass filter 560  Things to try out: –Square and triangle waves –Different resistor and capacitor values –Large signals (distortion!)

34. Measuring voltage as a function of time: The Oscilloscope Oscilloscope (‘scope) acts as a ‘time dependent volt- meter’. Allows visualisation of time variation of voltages Most scopes have two or more ‘channels’. Allows you to e.g. monitor input to a circuit and output from a circuit at the same time.

35. Errors!? I (/mA)V (/V) R=V/I (/  )R meas (/  ) 27.1±0.214.78±0.08545±6548±4 Measured current I=27.1mA Error=27.1*0.005+0.1=0.1355+0.1  I=0.2mA Measured voltage V=14.78V Error=14.78*0.005+0.01=0.0739+0.01  V=0.08V  I/I=0.2/27.1=0.0074  V/V=0.08/14.78=0.0054  R/R=sqrt(0.0074 2 +0.0054 2 )=0.00916≈0.009 R=V/I=14.78/(27.1  10 -3 )=545.4   R=0.009  545.4=5.9  Answer:R=545±6 