Electronics Applications of Kirchhoff’s Laws and AC Circuits in Lecture
Explore the lecture covering Kirchhoff’s laws, AC circuits, resistors, capacitors, RC circuits, and Fourier transforms in electronics. Learn about alternating current, waveforms, superposition, and Fourier transform examples, including NMR applications. Dive into circuit applications and waveform analysis in this informative session.
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Presentation Transcript
Announcements Website update Web version of homework Set 1 (now complete) I have posted solutions to Rubinson & Rubinson problems of set 1.1 I will post a data set soon for HW 1.2 problem Quiz 1 on 2/2 (related to lecture and HW 1.1 set) Additional Problems also due 2/2 Today s Lecture Continued application of Kirchhoff s laws AC and other time varying circuits Capacitors and RC circuits
Electronics Applications of Kirchhoff s Laws resistors in series and voltage divider (started last time) resistors in parallel more complicated circuits
Electronics Alternating Current DC = direct current (slowly varying voltage with time) AC = alternating current (produced by many electric generators In US 120V, 60 Hz is most common for AC outlet power Voltage (or current) time period time v = Vpeaksin t frequency = 1/(time period)
Electronics Alternating Current Related waveforms Square wave Sawtooth wave Voltage Voltage time time
Electronics Alternating Current Superposition and Fourier Transforms Vnet(t) = V1(t) + V2(t) Sine wave voltage transforms to single frequency See example Fourier Transform (of infinite wave) High frequency wave low frequency wave Sum (beat frequency) Amplitude high freq. low freq. 3 3 1 3 2 2 2 1 high freq. low freq. sum Amplitude 1 0 Amplitude Amplitude 0 high freq. low freq. 0 -1 -1 -1 -2 -2 -2 -3 -3 -3 0 50 100 150 200 0 50 50 100 time 150 150 200 0 100 200 time time frequency
Electronics Alternating Current Other Fourier Transform Examples Example seen in NMR Fourier Transform Non-infinite decay wave 1 Amplitude 0 Finite Width -1 0 50 100 150 200 time (s)
Electronics Alternating Current NMR Example cont. Most NMR FIDs look messier than shown Due to a) multiple peaks and b) noisy signal which leads to noisier specra To reduce the effect of the noise, it is common to increase the decay by multiplying the signal by an exponential decay function (Line Broadening in Bruker TopSpin software) FID processed with exponential decay Example of Noisier FID Fourier Transform signal rich region Non-infinite decay wave New spectrum has reduced noise but broader peak noise rich region 1 Amplitude 0 -1 0 50 100 150 200 time (s)
Electronics AC/Fourier Transform Question Which of the following signals when Fourier transformed will show the frequency pattern shown to the right? frequency
Electronics Capacitors Capacitors are devices to store charge capacitors are plates with small gap between plates charge spreads out along plate inducing opposite charge to other plate no dc current across gap (gap is non-conductive) 5 V Capacitance = C = q/V In capacitors, C = constant
Electronics Capacitors Uses of Capacitors Storage of charge to provided needed power Power supply may not supply enough power to start motor (start up power > running power) with capacitor, initial available I is high motor
Electronics Capacitors Use of Capacitors (continued) Analog data filter (RC filter low pass type shown) signal out signal in Reduction of high frequency noise (example is numerically done filter) FLD Plot (peak of interest) 1.06 1.04 FLD Signal Raw Data RC filtered (tau = 0.05 min.) 1.02 1 0.98 5 5.5 6 6.5 7 Time (min.)
Electronics RC Circuits An RC circuit consists of a resistor and capacitor in series You are responsible for quantitative understanding of behavior from step change in voltage (see below) 1) Before t = 0, switch in down position so V = 0 all parts but short segment 2) As switch is thrown (t = 0), charge travels through resistor to capacitor, but this takes time 3) After some time, the capacitor is fully charged and current drops to zero Switch V = 5V 5 V
