lab3

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Feb 20, 2024

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EEL4119L Electronics Laboratory II Experiment 3 By Pablo Sanchez James Saville Niv Barazani Nabil Elsrouji Charles Florestal October 15, 2019
Group 5 Experiment 3 2 | P a g e Table of Contents Abstract ........................................................................................................................................... 3 Equipment and Tools Used ............................................................................................................. 3 Components Used ........................................................................................................................... 4 A. Class C Amplifier ................................................................................................................... 5 Procedure .................................................................................................................................... 6 ADS Simulations ........................................................................................................................ 8 Case A: Class C Amplifier Laboratory Measurements (Q=25) ................................................ 10 Case B: Class C Amplifier Laboratory Measurements (Q=34) ................................................ 13 Conclusion ................................................................................................................................ 14 B. 830KHz Colpitts Oscillator ...................................................................................................... 16 Introduction ............................................................................................................................... 16 Part 1: Open Loop 830KHz Colpitts Oscillator ........................................................................ 18 Procedure and Simulations ................................................................................................... 18 Part 2: Close Loop 830KHz Colpitts Oscillator ....................................................................... 22 Procedure and Simulations ................................................................................................... 22 ADS Simulations ...................................................................................................................... 22 830KHz Colpitts Oscillator Lab Measurements; Open Loop ............................................... 27 830KHz Colpitts Oscillator Lab Measurements; Closed Loop ............................................ 33 Crystal Controlled Colpitts Oscillator (PCB) ............................................................................... 35 Conclusion ................................................................................................................................ 42 Lab Report - Questions & Answers .............................................................................................. 43 Acknowledgment .......................................................................................................................... 47 References ..................................................................................................................................... 48
Group 5 Experiment 3 3 | P a g e Abstract Throughout this experiment, we will be making use of the oscillating properties of the LC circuits to make a Class C amplifier and a Colpitts Oscillator, each of which have their own unique property. For the Class C Amplifier, the BJT in the amplifier acts like a switch that when activated, would provide energy to an underdamped system (in this case the LC resonant circuit) and will continue to do so every ‘n’ cycle as opposed to a set frequency. For the Colpitts oscillator, the output of the Common Emitter amplifier, which is emitted at a phase shift of 180°, is transferred back into the input with the use of a feedback network that ultimately results in a 360° phase shift, creating a positive feedback loop. For this circuit, the oscillation rate is determined by the LC circuit. Equipment and Tools Used This experiment used different instruments and measuring tools accessible through FAU’s Electrical Engineering Lab room 210 in order to measure the passive component values, power the BJT Amplifier and measure and observe the behavior of both the Class C Amplifier and the Colpitts Oscillator. Furthermore, some additional tools were used to assemble one of the Colpitts Oscillator to a through-hole circuit board: • GW INSTEK GDM -8245 – Dual Display Digital Multimeter • GW INST EK GFG-3015 – Function Generator • GW INSTEK GPS -3303 – 3 Channel Laboratory DC Power Supply • Tektronix TDS 2012C – Two Channel Digital Storage Oscilloscope
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Group 5 Experiment 3 4 | P a g e • Tektronix MDO3024 – Mixed Domain Oscilloscope • Tektronix TPP0250 - Voltage Scope Probe • Scope Probe • Banana Cable (BNC) to Pin • Voltmeter Probe • Soldering Iron • Solder • Wire Cutter/Clippers Components Used • ¼ W Resistors – Precision ±1% Metal Film • ¼ W Capacitors (Electrolytic, Multi -Layered Ceramic, Tantalum) • Inductors • 2N3904 & P N2222A NPN Bipolar Junction Transistor • Breadboard • Jumper Cable • Hakko 550 ֯ F Soldering Iron
Group 5 Experiment 3 5 | P a g e A. Class C Amplifier This experiment brings upon us a new component. The inductor has been theoretically studied by students in the past, but this will be the first time we get to physically handle them. This part of the experiment will teach us tuning of circuits to get the results we desire. We have been given design requirements with a specific circuit in mind. This circuit will include and inductor, resistors, and capacitors. They will form to build a Class C Amplifier. This amplifier should be displayed with the certain frequencies, resistances and capacitances to achieve certain Q values. Figure A1: Simple Class C Amplifier and Operating Curve (Amplifier Classes, 2019) Ideally this circuit should not dissipate any power, but in the real-world it dissipates enough energy to maintain efficiency. The transistor is the component that will do most of the dissipating since it will get surges of energy injected into it.
Group 5 Experiment 3 6 | P a g e Procedure The first step to beginning this project is to achieve the desired Q values. This will be done by calculating the resistor values at certain frequencies with certain capacitances. It requires building a circuit a simple RLC circuit with the resistor in line with the inductor and capacitor in parallel. It takes two-decade boxes: one capacitance and one resistance. This process involves tuning the frequency to get the input and output oscillations in phase. This means they will be at 0 degrees. The next step of tuning requires the output voltage exactly half of the input voltage by changing the resistance values with the decade box. The equation to calculate ? ? ∶ ? ? = 1 2𝜋√?𝐶 Then use the resistor values found from tuning and the ? ? to calculate the Q values using: ? = 2𝜋? ? ?𝐶 Table A1: Simple Class C Amplifier R and Q Values Nom+B5:G12inal C (Decade Boxes) Calculated fo f_0=1/(2π√LC) [Hz] Measured f0 [Hz] Measured C (decade boxes)[F] Measured Rs (decade boxes) [Ω] Calculated Q (from measured values) Q = 2pif0RC 17nf 55715.37 54300 1.7E-08 7200 41.7600602 15nf 59313.54528 58000 1.5E-08 8077 44.1518803 12nf 66314.55962 63700 1.2E-08 7600 36.5017881 10nf 72643.96 69920 0.00000001 5578 24.5052873 0.009uF 76573.46 72101 9E-09 6873 28.0227021 0.007uf 86826.14 83300 7E-09 7376 27.0236382 0.005uf 102734.07 92900 5E-09 7979 23.2870273 0.003uf 132629.12 113900 3E-09 9963 21.3902065 0.002uf 162436.83 138700 2E-09 10870 18.9459274 0.001uf 229720.37 173800 1E-09 13000 14.1962289
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Group 5 Experiment 3 7 | P a g e Figure A2: Class C Amplifier ADS Schematic Circuit Diagram Table A1: Active Mode Table for Class C Amplifier BJT Base Voltage ( 𝐕 𝐁 ) Junction Bias Active Mode? Q1 742 pV V C = 15 V Reverse Yes Q1 742 pV V E = 12.7 fV Forward Yes
Group 5 Experiment 3 8 | P a g e ADS Simulations The first simulation was run using a given Class C Amplifier circuit. It will be analyzed using a transient analysis. It will be fed an amplitude of 2.2V and a DC voltage of 15V. The frequency will be set at 72 kHz. Table A1, displays the voltages across the legs of the transistor. The table shows us that the transistor is in active mode across all spectrums. This can also be taken by the active mode expression where it shows the voltages greater than each other. 𝑉 ? < 𝑉 ? < 𝑉 ? Figure A3: Class C Amplifier ADS Simulations and Desired Values
Group 5 Experiment 3 9 | P a g e Table A2: Class C Amplifier – Simulation Calculations 1 𝑉 ??? = 𝑉 ??,?−? 2.8 12.79 V 2 𝐶????????? 𝐴???? (???) = ∆? × 360° ? 44.348 ℉ 3 ????𝑎? ????? (? ? ) = 𝑉??? 2 ?? 0.102 W 4 ?????? ????? (? 𝑖? ) = 𝑉 ?? × ? ? 0.105 W 5 𝐶????????? ?????????? (?) = ? ? × 100% ? 𝑖? 97.14 %
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Group 5 Experiment 3 10 | P a g e Case A: Class C Amplifier Laboratory Measurements (Q=25) The Class C amplifier is now being measured with a voltage input of 15V for the Q=25. The measurements will be taken with an ammeter running in series with the power supply. The 𝑉 ?? is found through observing the oscilloscope. The 𝑉 ?𝑀? is found through observing the oscilloscope as well. The resistor used for the Q=25 value is the 1% tolerance 5.6k resistor. Once we have all of these values, we can calculate or Conversion efficiency. The first step to finding the efficiency is to find the signal power. The Signal Power ( ? ? ) equation is listed below: ????𝑎? ????? (? ? ) = 𝑉 ??? 2 ? Once the Signal Power is found, the next step is to find the Supply Power ( ? 𝑖? ) : ?????? ????? (? 𝑖? ) = 𝑉 ?? ∗ ? ? Now that both the Signal and Supply Power have been calculated, the Conversion Efficiency ( ? )can be found: 𝐶????????? ?????????? (?) = ? ? ∗ 100% ? 𝑖? Our goal is to ideally achieve 100% efficiency, but because of our components not having ideal values the goal is to achieve 80% efficiency. Unfortunately, we were not able to meet the minimum of 80% efficiency due to, once again, the components did not have ideal values, the parasitic effects due to fluctuating voltages, and thermal runaway.
Group 5 Experiment 3 11 | P a g e Table A3: Conversion Efficiency Table for Class C Amplifier Q = 25 Voltage Levels I DC ?𝐴 V ?? V ?𝑀? ? ? 𝑖? ? ? Efficiency % 100% 6.60 36.2 V 13.0 V 5.65 k 0.0997 W 0.0299 W 30.0 % 80% 7 .76 31.0 V 11.2 V 5.65 k 0.117 W 0.0222 W 19.0 % 60% - - - - - - - 40% - - - - - - - 20% - - - - - - -
Group 5 Experiment 3 12 | P a g e Figure A4: Class C Amplifier Breadboard Figure A5: Class C Amplifier Breadboard Oscilloscope Simulation (Q=25)
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Group 5 Experiment 3 13 | P a g e Case B: Class C Amplifier Laboratory Measurements (Q=34) Table A4: Conversion Efficiency Table for Class C Amplifier Q = 34 Figure A6: Class C Amplifier Breadboard Oscilloscope Simulation (Q=34) Voltage Levels I DC ?𝐴 V ?? V ?𝑀? ? ? 𝑖? ? ? Efficiency % 100% 9.29 38.2 V 13.2 V 7.64 k 0.141 W 0.0228 W 16.2 % 80% 9.28 35.8 V 12.6 V 7.64 k 0.142 W 0.0208 W 14.6 % 60% 3 6.5 30.0 V 10.9 V 7.64 k 0.5585 W 0.01556 W 2.7 % 40% - - - - - - - 20% - - - - - - -
Group 5 Experiment 3 14 | P a g e Conclusion To conclude this experiment we wanted to mention that the primary objective was to obtain 100% efficiency (representing of at least 80% efficiency) for the Class C amplifier. We was not able to obtain the desired results due to many factors. As we mentioned before, ideal components were not used and what is meant by this is that the pas sive component’s values are not exact to our theoretical calculations. Interference may occur due to parasitic influences from the passive components and supply sources. One thing that also might be noted, is that when tuning the amplifier, varying the frequency is a bit course rather fine tuning and the circuit reacts relatively quickly when meeting a certain threshold. Due to this reason, we were not able to collect more data for our tables. When tuning the circuit in attempt to find where the emitter and output voltage readings would drop completely, we found that at an approximate input voltage signal of 40 mVp-p and an input frequency of about 43.5 kHz this would occur (Q=34). This would also occur for Q = 25, at an input voltage signal of about 30 mVp-p and input frequency of about 68.7 kHz. Another event worth documenting is when tuning the circuit, at a given frequency near the drop out threshold, the readings on the ammeter for the collector started slowly rising over time. This indicated that the transistor began experiencing something that is called thermal runaway. This is a cycle where the collector current increases and causes the transistor to dissipate more power which in turn cause the transistor’s temperature to increase. Eventually the tran sistor would self- destruct. A method to correct this is through better biasing of the transistor and an added negative feedback for stabilizing the biasing. We were able to obtain voltage levels that represented our theoretical calculations, whereas the collector voltage generated a voltage that was at most around 2 times as much as the
Group 5 Experiment 3 15 | P a g e supply voltage. To obtain the best possible efficiency we want to get the maximum voltage (Vc = 2Vs) out on the transistor’s collector while the current is at its minimum ( Idc = 0mA). This would yield the theoretical 100% efficiency.
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Group 5 Experiment 3 16 | P a g e B. 830KHz Colpitts Oscillator Introduction Figure B1: Simplified Colpitts Oscillator Schematic In Figure B1 shows a more simplified version of the Colpitts Oscillator and its Small Signal Equivalent circuit. We can see that the feedback of the Colpitts Oscillator comes from the base of the BJT with a resistor. In order to show that the circuit will operate as an oscillator, we must apply the Barkhausen condition. The Barkhausen condition states that if a closed-loop circuit has a sinusoidal input with a feedback signal at which it is in phase and greater than or equal to the reference input at any one frequency, then the circuit is considered unstable. Applying the Barkhausen condition to the Colpitts Oscillator, we are given two nodal equations provided below, where the input sinusoidal signal 𝑉 ? is equal to the feedback voltage 𝑉 𝑓𝑏 . (1) − ? ? 𝑉 ? = 𝑉 ? (?𝜔𝐶 1 + 1 ?𝜔? ) − 𝑉 ? ( 1 ?𝜔? ) (2) 0 = −𝑉 ? ( 1 ?𝜔? ) + 𝑉 ? ( 1 ?𝜔? + ?𝜔𝐶 2 + 1 ? + ? 𝜋 ) + _ v s C 1 C 2 L C 2 C 1 L R I r r R gV m s V f b A B
Group 5 Experiment 3 17 | P a g e After some algebra manipulation and substitution, we get the resulting equation in terms of 𝑉 ? as shown below. (3) 𝑉 ? { 𝐶 1 + 𝐶 2 ? − 𝜔 2 𝐶 1 𝐶 2 + ? [ 𝜔𝐶 1 ? + ? 𝜋 − 1 𝜔?(? + ? 𝜋 ) ]} = 𝑉 ? [ −? ? ? 𝜋 ?𝜔?(? + ? 𝜋 ] Analyzing the equation above, we can see that the right-hand side has no real part in which the left-hand s ide’s real part must be equal to 0. This will only happen at one frequency which we will label as 𝜔 ? . 𝜔 ? = √ 𝐶 1 + 𝐶 2 ?𝐶 1 𝐶 2 Lastly, we need to make sure that the final condition is met. Which means we must have the imaginary part of equation (3) be equal since the real part of the left-hand side is equal to 0. Doing that gives us the resulting equation below. (4) 𝜔𝐶 1 ? + ? 𝜋 − 1 𝜔?(? + ? 𝜋 ) = ? ? ? 𝜋 𝜔?(? + ? 𝜋 Substituting the equation for 𝜔 ? into equation (4), it will equate the following equation below. ? ? ? 𝜋 = 𝛽 = 𝐶 1 𝐶 2 In our experiment, we want to have oscillations to occur at 𝜔 ? = 830KHz. We were already given values that are very close to having oscillation to our desired frequency of 830KHz. We move onto simulating our Colpitts Oscillator in ADS.
Group 5 Experiment 3 18 | P a g e Part 1: Open Loop 830KHz Colpitts Oscillator Procedure and Simulations Before creating our schematic onto ADS, we must list the values corresponding to the appropriate components of our Open Loop 830KHz Colpitts Oscillator. List of Components with values ? 1 = 144?𝛺 ? 2 = 47?𝛺 ? 3 = 1.2?𝛺 ? 4 = 10?𝛺 ? 5 = 10?𝛺 ? 6 & ? 7 = 470𝛺 𝐶 1 & 𝐶 7 = 100?? 𝐶 2 & 𝐶 4 = 1?? 𝐶 3 = 10?? 𝐶 5 & 𝐶 6 = 1𝜇? ? 1 = 40𝜇𝐻 ? 2 = 100?𝐻 Now with the components that we have listed, we can conduct our schematic of the Open Loop Colpitts Oscillator and run an AC Sweep to see at which frequencies it oscillates at.
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Group 5 Experiment 3 19 | P a g e Figure B2: ADS Schematic of Open-Loop 830KHz Colpitts Oscillator Table B1: Active Mode Table of Open Loop 830KHz Colpitts Oscillator BJT: Base Voltage: Junction: Bias: Active mode? Q1 VB = 3.92 V VC = 18 V Reverse Yes Q1 VB = 3.92 V VE = 3.25 V Forward Yes Q2 VB = 8.58 V VC = 18 V Reverse Yes Q2 VB = 7.86 V VE = 7.86 V Forward Yes As you can see in Figure B2 that the circuit looks different compared to the Colpitts Oscillator circuit in Figure B1. The additional components are added because we do not have an Ideal Current source and we are making use of what we have in the lab. Now we can simulate our schematic and observe at which frequencies the oscillations will occur.
Group 5 Experiment 3 20 | P a g e Figure B3: AC Sweep Plots of 830KHz Open Loop Colpitts Oscillator Observing the graphs in Figure B3, we can see that in the AC sweep graph the Open Loop Colpitts Oscillator oscillates at frequencies 4.454KHz with a gain of 53dB and 831.8KHz with a gain of 49.320dB. Looking at the phase plot of the Open Loop Colpitts Oscillator in Figure B3, we see that the two resonances happen around the same frequency that the Colpitts Oscillator oscillates.
Group 5 Experiment 3 21 | P a g e These two resonances are caused by the specific capacitors near the 40uH inductor. If you eliminate all the capacitors at which the collector node of the first BJT is connected to the base node of the second BJT, then no resonance will occur. This is also proven mathematically in the equations provided in the introduction. Therefore, at which frequencies the resonance occur at are dependent on the capacitance value of the capacitors near the 40uH inductor.
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Group 5 Experiment 3 22 | P a g e Part 2: Close Loop 830KHz Colpitts Oscillator Procedure and Simulations ADS Simulations Figure B4: Closed-Loop Colpitts Oscillator In part 2, we are asked to run a stimulation for the Closed Loop Colpitt Oscillator. Noticed how compared to our open loop colpitt, there is an added capacitor. Next were asked to run the stimulation in ADS. Down below we have ADS stimulations.
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Group 5 Experiment 3 23 | P a g e Figure B5: Closed-Loop Colpitts Oscillator Circuit An oscillator is a feedback system composed of a forward path with gain and a feedback path with gain. The Colpitts Oscillator design uses two capacitors in series with a parallel inductor to form its resonance tank circuit producing sinusoidal oscillations. We can see that the c ircuit above has feedback and will be operating in “close loop” mode.
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Group 5 24 | P a g e Figure B6: Closed-Loop Colpitts Oscillator DC Bias After running our simulation, we can see that our BJT is in Active mode. We ran a transient stimulation to show indeed our closed-loop circuit would oscillate. The DC analysis has been included above.
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Group 5 Experiment 3 25 | P a g e Figure B7: Closed-Loop Colpitts Oscillator Circuit Response The period, which is T, is equal to m3 – m2 according to figure B4, our records indicate that frequency oscillation occurs roughly at 840 kHz.
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Group 5 Experiment 3 26 | P a g e Figure B8: Closed-Loop Colpitts Oscillator Circuit Response The Colpitts oscillator does operate where it was expected to just primarily looking at the frequency response of the AC input. You then realize that when you look to verify the Barkhausen condition, it is roughly the frequency we expected it to be from our calculated value. To help determine the expected frequency, we can go ahead and use the following formula: We can see from our schematic above that C4 & C6 are 1nf and 10nF capacitors and our inductor is 40uH. With this, we calculated our expected frequency to be approximately f o = 𝑤 ? 2𝜋 = √ (1∗10 −9 )(10∗10 −9 ) (40∗10 −6 )(1∗10 −9 )(10∗10 −9 ) = 5244044.2 2𝜋 = 834.6 kHz The oscillation frequency as predicted by ADS was 840.00 kHz.
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Group 5 Experiment 3 27 | P a g e 830KHz Colpitts Oscillator Lab Measurements; Open Loop Before we conduct our experiment, we must first measure all our components that we will be using for our Open Loop Colpitts Oscillator. Table B2: Measured Components for Open Loop 830KHz Colpitts Oscillator Component Value Measured Value ? 1 144KΩ 145.2 KΩ ? 2 47KΩ 46.54KΩ ? 3 1.2KΩ 1.188KΩ ? 4 10KΩ 9.91KΩ ? 5 10KΩ 9.815KΩ ? 6 470Ω 469.6Ω ? 7 470Ω 466.1Ω 𝐶 1 100nF 97.2nF 𝐶 2 1nF 1.033nF 𝐶 3 10nF 9.85nF 𝐶 4 1nF 1.033nF 𝐶 5 1μF 0.97μF 𝐶 6 1μF 0.993μF 𝐶 7 100nF 98.8nF ? 1 40μH 39.1μH ? 2 100mH 79mH 𝑉 ?? 18V 18.13V Now we can assemble the Open Loop Colpitts Oscillator onto a breadboard and take scope images of 𝑉 ??? at two certain frequencies at which it oscillates. We will also conduct and AC Sweep and observe the gain from the input to the output. Plus, we need to analyze the phase and determine how it relates to oscillation.
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Group 5 Experiment 3 28 | P a g e Figure B9: Picture of Assembled Open Loop 830KHz Colpitts Oscillator Table B3: Measured Voltage at the Transistor Pins of the Open Loop 830KHz Colpitts Oscillator Transistor Pin Measured Voltage Q1 Base 3.772V Q1 Collector 17.49V Q1 Emitter 3.266V Q2 Base 8.715V Q2 Emitter 18.13V Q2 Emitter 8.041V The image shown in Figure B9 is the assembled Open Loop 830KHz Colpitts Oscillator on a breadboard with its corresponding transistor pin voltages given in Table B3.
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Group 5 Experiment 3 29 | P a g e Figure B9:830KHz Open Loop Colpitts Oscillator; Oscilloscope Image of 𝑉 ??? at 5.967KHz As we can see with the image shown above in Figure B9, we achieved a peak gain of 36.48dB at 5.967KHz. Comparing this with our ADS results, the lower resonance frequency was at 4.545KHz and had a gain of 53dB. There could be several factors as to why we could not achieve that gain and why the lower resonance frequency between actual vs ADS differ by 1.4KHz in which we will discuss later in the experiment. Figure B10: 830KHz Colpitts Oscillator; Oscilloscope Image of 𝑉 ??? at 848.9KHz
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Group 5 Experiment 3 30 | P a g e Analyzing the scope image of the output in Figure B10, we can see that the higher resonance frequency occurs at 848.9KHz instead of the predicted 830KHz. Interestingly, the higher resonance frequency achieved a gain of 37.96dB which was higher that the gain in the lower resonance frequency. This was a surprise since ADS simulated that the lower resonance frequency would have a higher gain than the higher resonance frequency. Now we will conduct an AC Sweep and we should see gain increases when it gets close to both resonance frequencies at 5.967KHz and 848.9KHz. Also, the phase should be relatively close to zero since the input and output will be in phase when the circuit oscillates. Table B2: Measured AC Sweep of 830KHz Open Loop Colpitts Oscillator Freq (Hz) Vo (V) Vin (V) Gain (dB) Phase 100 52.0mV 3.20mV 24.22 ? 200 48mV 4mV 21.58 ? 300 10mV 26mV -8.30 ? 400 6mV 22mV -11.29 ? 450 5.6mV 26.4mV -13.47 ? 475 7.2mV 26.0mV -11.15 ? 490 8.8mV 26.0mV -9.41 ? 495 14.0mV 27mV -5.70 ? 500 14.0mV 27mV -5.70 ? 800 20.0mV 27.0mV -2.61 ? 900 20.0mV 27.0mV -2.61 ? 1000 23.2mV 27.2mV -1.38 ? 1100 22.6mV 28.0mV -1.86 ? 1200 24.2mV 27.2mV -1.02 ? 1300 14.0mV 27.0mV -5.70 ? 1500 15.0mV 27.0mV -5.11 ? 1700 23.2mV 27.0mV -1.32 ? 2000 24.0mV 27.2mV -1.09 ? 2500 40.8mV 27.0mV 3.59 ? 3000 43.5mV 27.2mV 4.08 ? 4000 124.5mV 26.7mV 13.37 110 5000 453.6mV 27.2mV 24.44 80 6000 1.74V 23.3mV 37.46 6 7000 1.25V 27.5mV 33.15 -68 8000 960mV 27.4mV 30.89 -85 9000 870.0mV 27.2mV 30.10 -90 10000 836.1mV 27.7mV 29.60 -98 11000 830.0mV 27.6mV 29.56 -102
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Group 5 Experiment 3 31 | P a g e 12000 835.7mV 27.6mV 29.62 -120 13000 840.0mV 27.4mV 29.73 -123 14000 852.0mV 27.7mV 29.76 -120 14500 860.1mV 27.2mV 30.00 -121 15000 863.1mV 27.4mV 29.97 -124 16000 880.0mV 27.6mV 30.07 -138 17000 890.2mV 27.5mV 30.20 -141 18000 902.3mV 27.6mV 30.29 -145 19000 913.9mV 27.6mV 30.40 -139 20000 920.1mV 27.7mV 30.43 -140 21000 927.3mV 27.6mV 30.53 -156 22000 947.1mV 27.6mV 30.71 -159 23000 947.1mV 28.6mV 30.40 -150 24000 946.7mV 27.7mV 30.67 -152 25000 947.0mV 27.7mV 30.68 -155 35000 928.3mV 33.3mV 28.90 171 45000 854.8mV 28.2mV 29.63 158 50000 822.0mV 29.1mV 29.02 162 75000 650.1mV 27.8mV 27.38 138 100000 523.1mV 28.2mV 25.37 123 200000 295.1mV 28.4mV 20.33 106 750000 283.3mV 26.0mV 20.75 85 830000 844.0mV 35.2mV 27.60 62 1000000 158.5mV 23.5mV 16.58 -80 Figure B11: Excel Graph of Open Loop 830KHz Colpitts Oscillator AC Sweep Gain in dB -20 -10 0 10 20 30 40 50 100 300 450 490 500 900 1100 1300 1700 3000 5000 7000 9000 11000 13000 14500 16000 18000 20000 22000 24000 35000 50000 100000 750000 1000000 Gain (dB) Frequency (Hz) Gain in dB of Open Loop 830KHz Colpitts Oscillator Gain (dB)
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Group 5 Experiment 3 32 | P a g e Table 2 gives us a ton of data about the AC Sweep conducted onto the Open Loop 830KHz Colpitts Oscillator AC Sweep Gain in dB. To sum it up, Figure B11 puts all the data onto a line graph that looks like the graph provided to us by ADS in Figure B3. Oddly, we have a higher gain at lower frequencies which is an unexpected result. This could be due to the small amplitude at the input since we used a 10mV amplitude at the input. Furthermore, looking at the excel graph provided in Figure B11 we see that the oscillations happens around 6KHz and 850KHz which is close to where we predicted.
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Group 5 Experiment 3 33 | P a g e 830KHz Colpitts Oscillator Lab Measurements; Closed Loop After running our simulations, we moved on to test each component. We measured every component used in order to properly build our physical circuit. Our results can be seen below. Note series of resistors used to obtain nominal value. Component Value Measured Values C5 100 nF 100.2 nF R1 144 kohm 144 kohm R12 47 kohm 47.3 kohm L4 100 mH 100 mH L5 40 mH 40.2 mH R3 1.2 kohm 1.19 kohm C1 1nF 0.99nF C3 1 uF 1.12 uF C14 10 nF 10.1 nF C15 1 nF 1 nf R4 10 kohm 9.88 kohm R6 10 kohm 9.96 kohm R5 470 ohm 468.9 ohm R7 470 ohm 469.1 ohm C8 100 nF 100 nF Vdc 18 V 18 V Table B1: Nominal & Measured Component Values
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Group 5 Experiment 3 34 | P a g e Next, we moved on to assemble the closed-loop Colpitts circuit. Our physical board can be seen below. Figure B6: Closed-Loop Colpitt Breadboard The laboratory report manual states to close the loop through the 1 uF input capacitor (removing the function generator and connecting Vin to Vout). Figure B7: Closed-Loop Colpitt Oscillation Frequency of 855.4 kHz
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Group 5 Experiment 3 35 | P a g e Crystal Controlled Colpitts Oscillator (PCB) I began by inserting the given schematic into my ADS schematic capture software. I then began the simulation. Figure 1 – Crystal Controlled Colpitts Oscillator In figure 1 I am showing the schematic as captured into the ADS software, with the DC Bias voltages showing. BJT Base Voltage: Junction: Bias: Active mode condition met? Q1 𝑉 ? = 11𝑉 𝑉 ? = 10.2𝑉 Forward No Q1 𝑉 ? = 11𝑉 𝑉 ? = 10.1𝑉 Forward Yes Q2 𝑉 ? = 8.79𝑉 𝑉 ? = 12𝑉 Reverse Yes Q2 𝑉 ? = 8.79𝑉 𝑉 ? = 8.05𝑉 Forward Yes Figure 2 – Active mode table, 100mV differential input. In Figure 2 the active mode table shows that Q1 is in saturation mode while Q2 is in active mode.
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Group 5 Experiment 3 36 | P a g e Figure 3 – Time Domain Transient Simulation In Figure 3 I am showing the time domain output of the simulation of the crystal-controlled oscillator circuit. Here we can see that the amplitude of the output is 3.530V peak to peak.
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Group 5 Experiment 3 37 | P a g e Figure 4 – Frequency domain plot of the transient simulation In Figure 4, I have used the data produced by the transient simulation in a frequency domain plot to view the frequencies generated by this circuit. We can see that the primary frequency emitted is centered at 16.25 MHz, with very little noise spiking up in the harmonic frequencies. After testing the circuit in the simulation by ADS, I then used KiCAD to produce my PCB design.
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Group 5 Experiment 3 38 | P a g e Figure 5 – KiCAD Schematic for PCB Layout Figure 5 shows the schematic used to generate the PCB design. Figure 6 – PCB Layout Produced with KiCAD In Figure 6 I am showing the PCB layout designed using KiCAD. I have included a socketed connection for the Crystal and an SMA output with wired test points and power supply inputs.
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Group 5 Experiment 3 39 | P a g e Next, I went on to select and measure the 1% components for my circuit. Reference Nominal Value Measured Value RB1 5.6k Ω 5.61 kΩ RB2 27 kΩ 26.9 kΩ RC1 100 Ω 100.7 kΩ RE1 1 kΩ 1 kΩ RB3 1 kΩ 999.7 Ω RE2 470 Ω 468.3 kΩ RL1 100 kΩ 100 kΩ C1 100 pF 0.11 nF C2 100 pF 0.107 nF C3 47 pF 0.043 nF Figure 7 – Components Table Figure 7 shows the components used in constructing the crystal-controlled oscillator. Figure 8 – Assembled PCB of Crystal-Controlled Oscillator After assembling the PCB, I tested it out with a 16MHz Fundamental crystal, and also a 36MHz 3 rd overtone crystal. Both crystals produced oscillations at their nominal frequency, and both had comparable DC bias voltages when measurements were taken.
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Group 5 Experiment 3 40 | P a g e BJT Base Voltage: Junction: Bias: Active mode condition met? Q1 𝑉 ? = 9.56𝑉 𝑉 ? = 11.1𝑉 Reverse Yes Q1 𝑉 ? = 9.56𝑉 𝑉 ? = 8.87𝑉 Forward Yes Q2 𝑉 ? = 8.8𝑉 𝑉 ? = 12𝑉 Reverse Yes Q2 𝑉 ? = 8.8𝑉 𝑉 ? = 8.05𝑉 Forward Yes Figure 9 – Active mode table, measured values. With both crystals, my measured values differed from the simulation. Also, with both crystals, the DC measured values revealed both transistors to be in the active mode. I experimented with ADS and found that with the simulated crystal disconnected from the circuit, my measured DC bias voltages matched the simulation. This was contradictory since due to my oscilloscope readings; I was able to confirm my circuit working correctly and oscillating correctly. This led me to the conclusion that the simulated crystal’s impedance was different than my actual crystal impedance, so I continued with the experiment. Figure 10 – Experimental DC simulation without the crystal. In figure 10, I am showing the simulation results used in comparing to my measured values with the crystal removed from the circuit. This more closely matched my actual bias voltages.
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Group 5 Experiment 3 41 | P a g e Figure 11 – Oscilloscope image of output oscillations In Figure 11 We can see that the 16MHz crystal is causing the 16MHz output despite the difference in bias voltages. I predict that this is due to a difference in crystal impedance from actual to simulated values of the ADS crystal model.
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Group 5 Experiment 3 42 | P a g e Conclusion Overall, our values obtained from our stimulated breadboard compared to our stimulation ADS values were really close. The variation could have been from possibly our components used when making the breadboard, for example the series of resistors that made 144 K Ω , or equipment used. The Colpitts Oscillator resonance frequencies are very sensitive due to the values of the capacitor that are near the 40μH inductor . Therefore, the respective tolerance that the capacitors have could be the reason why the measured resonance frequencies were a few kilohertz away from the expected resonance frequencies obtained from the simulated results in ADS. Parasitic interference from the plastic breadboard could have also caused the lower measured gains in the actual Colpitts Oscillator compared to expected gains in ADS. So, removing the input sine wave, and shorting the output we can see our diagram shows a very nice oscillation, with a frequency of 855.4 kHz. It’s very close to what we expected of 840 kHz (calculated frequency). None the less it comes quite close to our measured value and meets the Barkhausen condition.
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Group 5 Experiment 3 43 | P a g e Lab Report - Questions & Answers Questions 1. Comment on the efficiency of the Class C amplifier for different values of Vrms. Explain why it should increase or decrease. 2. (Research Question) Comment on a practical application of varying VCC at a low frequency while a high frequency signal is applied at the input of a Class C amplifier. Can you write down an equation for the output voltage? 3. What is the relationship of with the ratio of the capacitors that allows oscillation in the Colpitts oscillator? 4. What is the purpose of the 1-ohm resistor in the emitter of the Class C Amplifier circuit? 5. Measurements were made of a resistance R at different frequencies. Explain what resistance R is used for when calculating the efficiency of the Class C Amplifier. 6. How does the measured oscillation frequency of the Colpitts oscillator compare with the theoretical prediction of Equation (12) for each set of capacitances and inductance? Explain any discrepancies. Would you expect the observed oscillation frequencies to be higher or lower than the theoretically predicted values? Why? 7. Why is the Crystal Controlled Oscillator considered to be very stable? 8. Explain the meaning of a 3rd overtone crystal. 9.
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Group 5 Experiment 3 44 | P a g e Answers: 1.) Since the impedance R of the RLC circuit remains relatively constant at the set resonant frequency, the only other aspect that contributes to the output power is the output signal’s amplitude, or specifically, its RMS value. Given that: ? ? = ? 2 ??? ? ⟹ ? = ? ? ? 𝑖? = ? 2 ??? /? ? 𝑐𝑐 / 𝑖 𝑐 Since the output is really the only aspect of the efficiency that changes, then it can be inferred that as the output signal decreases, so does the efficiency and the opposite holds true. 2.) When inputting a varying VCC at low frequency while a high frequency signal is applied to the input of a Class C amplifier, a real-life application of this would be used for tuning circuits for some sort of frequency applications such as radio or communications. The AC input enters the base of the BJT and the amplified Vo will show up at the collector. (Power Amplifiers) 𝑉 ? = 𝑉 ?? ? 2𝜋 ( 1 − cosθ 2? − ???2? ) 3.) According to the Barkhausen criterion, the following expression must be satisfied for oscillation to occur: 𝐴 ? ≥ 1 𝛽 where β (beta) is the feedback ratio of capacitor C1 and C2 in series: 𝛽 = C1 C2
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Group 5 Experiment 3 45 | P a g e 4.) The 1-ohm resistor will give a proportional reading for the current passing through the emitter, this will allow you to correctly monitor the current at the emitter and its levels. 5.) When calculating the efficiency of the Class C Amplifier, the resistance R is used to transform the source resistance. It was found through tuning the input frequency along with a specific capacitance. Once the input and output signals were in phase meaning the phase is at 0 degrees, then the tuning of resistance to achieve the output voltage product of half the input voltage. 6.) For the Colpitts Oscillator, we learned the oscillating frequency is determined by the LC tank on the output of the circuit; for closed loop, in the feedback loop of the circuit. We also saw that the oscillating frequency differed between the ADS simulation and breadboarded measured results. The 3 reasons for this are first, the real-world tolerance given to analog components in which the part value can vary between a given deviation. Second, the inductor has a real-world voltage loss associated with it. And third, the parasitic capacitance and impedance when using a breadboard can easily deter the circuit’s ability to be precise. 7.) The Crystal controlled oscillator is much more stable and accurate due to the crystal controlling the oscillations. The crystal is much more finely tuned and calibrated for this and will outperform an RLC tank made up of 1% components. We find that the crystal will also maintain its rated frequency with variations in both resistance and capacitance of the circuit, and is not nearly as reliant on component values as designs that do not use a crystal.
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Group 5 Experiment 3 46 | P a g e 8.) According to an engineering article from Microsemi, Fundamental crystals vibrate at the frequency they are “designed for”, while 3 rd overtone crystals vibrate at 3 times their fundamental frequency. This has to do with the difficulty of manufacturing fundamental crystals in higher frequencies. By manufacturing 3 rd overtone crystals, manufacturers are able to have thicker crystals resulting in less breakage. A fundamental crystal would be much thinner than a 3 rd overtone crystal vibrating at the same frequency. By utilizing a harmonic of the crystal they are able to create much higher frequencies without taking the manufacturing risks of breakage during processing.
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Group 5 Experiment 3 47 | P a g e Acknowledgment We would like to thank Dr. Peterson for his knowledge and time taken to help us troubleshoot and execute this project.
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Group 5 Experiment 3 48 | P a g e References Amplifier Classes and the Classification of Amplifiers. (2019, June 10). Retrieved from https://www.electronics-tutorials.ws/amplifier/amplifier-classes.html . http://web.mit.edu/klund/www/weblatex/node4.html Fundamental vs 3 rd Overtone (2017, January 30 th ) Maggie Ford. Retrieved from http://microsemi.com/blog/2017/01/30/fundamental-vs-3rd-overtone/ Power Amplifiers. Retrieved from https://pdfs.semanticscholar.org/c38c/003f4efddc1ef44038fa25e75894872939a7.pdf
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