Decibel (Db) – 3Db Point

Lab & Checkoff Logistics

• Open lab with no scheduled lab sessions –lab can be done any time the lab is open. • Start early –32 students with 17 + 6 lab stations • Staffed lab hours posted. • Tools & Safety •Resonance 2 handouts • Material on cart and round table; additional • Bode Plots lecture notes parts available from parts bins near the center • Wires –theory vs reality pset1 • Amplitude Modulation columns and from EDS 38‐500. • Diodes • Lab reports should be turned in for grading. Acknowledgements: Lecture material adapted from Prof Qing Hu & Prof Jae Lim, 6.003 Figures and images used in these lecture notes by permission, copyright 1997 by Alan V. Oppenheim and Alan S. Willsky

6.101 Spring 2020 Lecture 2 1 6.101 Spring 2020 2

Tools & Safety Decibel (dB) –3dB point • Correct tools makes life easier! V   P  • Understand power ratings. dB  20log o  dB 10log o     P  Vi  i  • All EECS Instructional Laboratories lab kit voltages are   below 50 volts peak or 50 volts DC. See staff if you are working with voltages greater than 50 volts. 100 dB = 100,000 = 105 log10(2)=.301 • All students must read and sign the safety form 80 dB = 10,000 = 104 https : / / eecs‐ug.scripts.mit.edu:444/safety/index.py/6.101 3 dB point = ? 60 dB = 1,000 = 103 half power point 40 dB = 100 = 102

6.101 Spring 2020 3 6.101 Spring 2020 Lecture 2 4 Resonance (Series RLC) –Key points Bandwidth and Q (Series RLC)

  R • BW (hertz) = h  l  • Applies to more complex RLC 2 2L + RL circuits V C - •At resonance: power is maximum •Q* (quality factor, radians) resonant frequency bandwidth 1  1 Z  R  sL   R  j( L  ) •At resonance: phase angle zero, 1  L  sC C Q    i.e. capacitive reactance = R  C  inductive reactance, or impedance is real •Higher Q implies more selectivity

*Agarwal/Lang Foundation of Analog Digital Elect Circuits equation 14.47, p 794

6.101 Spring 2020 Lecture 2 5 6.101 Spring 2020 Lecture 2 6

Summary – Parallel Series RLC Series Parallel Duality

Parallel Series R L 1 1 + f  I O fO  V C RL CV 2 LC 2 LC I - 2 f L Q  2 f RC Q  O o R 1  1   1 1  R V  I R  jwL   I  V   jwC BW  ( fh  fl )  BW  ( f  f )  jwC   2RC h l 2L    R jwL   1 Series Parallel   2 f 0 LC  0 VI 1 R1/R f0  LC 2 LC CL

6.101 Spring 2020 Lecture 2 7 6.101 Spring 2020 8 Bode Plot ‐ Review

• A Bode plot is a graph of the magnitude (in dB) or phase of the transfer function versus frequency. • Magnitude plot on log‐log scale – Slope: 20dB/decade, same as 6dB/octave • Bode plot provides insight into impact of RLC in frequency response. • Stable networks must always have poles and zeroes in the left‐half plane.

https://web.njit.edu/~levyr/Physics_121/chapter32.ppt

6.101 Spring 2020 9 6.101 Spring 2020 Lecture 2 10

MATLAB MATLAB commands

• % comment delimiter • Matlab windows: • MATLAB arrays starts with index=1 current folder, – command, work a = [4,5,6] is a row vector a(2)=5 space (workspace), – b = [7;8;9] is a column vector command history • “;” don’t print values (commandhistory) • Variables are case sensitive • Set folder to your • Variables must start with a letter Aa favorite folder • who/whos: list the current variables in short/long form • Built in help in • shg – show recent graph, pop to the front command window • use apostrophes for FILENAME • docking/undocking • format shortENG – display engineering notation Command window Workspace

Current folder Command history MATLAB MATLAB Matrix Operation

>> a=[2,3,4] pi 3.14159265 a = 2 3 4 i,j sqrt(-1) imaginary unit >> b=[1,0,0] b = 1 0 0 zeros(n,m) an n x m matrix of zeros >> c=a+b ones(n,m) an n x m matrix of ones c = 3 3 4 >> d=a*b % dot product operation ??? Error using ==> mtimes + - addition, subtraction Inner matrix dimensions must agree. */ ^ multiplication, division, power >> d=a.*b d = 2 0 0 sqrt square root >> e=a*b' % ' transpose e = 2

MATLAB Flow Control MATLAB example sin(x)

>> t=[0:1/100:1-1/100]; % create t from 0 to .99, 100 values if a == 0 >> x=sin(2*pi*t); • if else statement b = a; >> plot(t, x); else >> stem(t,x); b = 1/a; >> shg end

• for loop n = 100 for m = 1:n a(m) = a(m) + 1; end • while loop n = 10 while n > 0 n = n – 1 end Bode vs Freqs Plots

MATLAB Functions bode, freqs format shortENG num=[1/L 0] denom=[1 R/L 1/(L*C)] 1 f=1/(2*pi*sqrt(L*C)) w=2*pi*f 1 • BODE(SYS,W) uses the vector W of frequencies (in radians/TimeUnit) to w_range = [.8*w:20:1.2*w]; evaluate the frequency response h=bode(num,denom,w_range); magh=abs(h); plot(w_range,magh) R=1 L=47uh C=1.8nf f=540khz • [MAG,PHASE] = BODE(SYS,W) and [MAG,PHASE,W] = BODE(SYS) return the shg freqs(num,denom,w_range) response magnitudes and phases in degrees (along with the frequency vector W if unspecified).

• SYS is the transfer function expressed as numerator and denominator in the form d  eS SYS  aS2  bS c • bode(num,denom,range) num=[d e], denom=[a b c], range= desired freqencies in radians

• freqs(num,denom,range) plots frequency response and phase angle

bode freqs not same scale 6.101 Spring 2020 17 6.101 Spring 2020 Lecture 2 18

Bode in Hz Selectivity and Q 1 R=1 L=47uh C=1.8nf 1 f=540khz

L=47uh C=1.8nf

[Mag, Phase, W] = bode(num, denom, w_range); f=540khz Freq_Hz = W/2/pi; Mag_dB = 20*log10(Mag); subplot(2,1,1) semilogx(Freq_Hz, Mag_dB) RQ title('Bode Diagram') ylabel('Magnitude (dB)') 1 160 subplot(2,1,2) semilogx(Freq_Hz,Phase) 532 xlabel('Frequency (Hz)') ylabel('Phase (deg)') 10 16 shg

6.101 Spring 2020 Lecture 2 19 6.101 Spring 2020 Lecture 2 20 r=1 l=4.7e-5 bw1=1/(2*pi*l) Selectivity and Q c=1.8482e-009 q1=f/bw1 num=[1/l 0] bw5=5/(2*pi*l) denom=[1 r/l 1/(l*c)] q5=f/bw5 f=1/(2*pi*sqrt(l*c)) bw10=10/(2*pi*l) w=2*pi*f q10=f/bw10 w_range = [.8*w:20:1.2*w] L=47uh [w,mag1]=bode_gh(1,l,c) >> bw1=1/(2*pi*l) [w,mag5]=bode_gh(5,l,c) bw1 = 3.3863e+003 C=1.8nf [w,mag10]=bode_gh(10,l,c) >> f f=540khz hold on f = 5.4000e+005 plot(w,mag1) >> q1=f/bw1 plot(w,mag5/max(mag5),'r-') q1 = 159.4683 RQ shg >> bw5=5/(2*pi*l) plot(w,mag10/max(mag10),'g-') bw5 = 1.6931e+004 1 160 shg >> q5=f/bw5 xlabel('w(rad/sec)') q5 = 31.8937 532 shg >> bw10=10/(2*pi*l) ylabel('Amplitude') bw10 = 3.3863e+004 10 16 shg >> q10=f/bw10 title(' Response for RLC series circuit') q10 = 15.9468 shg

6.101 Spring 2020 21 6.101 Spring 2020 Lecture 2 22

Lab 1 Topics Proper External Grounding for Lab 1 IF Transformer

• Resonance, Q, bandwidth • Transformers and impact on load and PC Board pri sec bandwidth NC • Diode detector, demodulation

• Simple AM transmitter and receiver Can

6.101 Spring 2020 23 6.101 Spring 2020 Lecture 2 24 Schematics & Wiring Wire Gauge

• IC power supply connections generally not drawn. • Wire gauge: diameter is inversely proportional to the All integrated circuits need power! wire gauge number. Diameter increases as the wire gauge decreases. 2, 1, 0, 00, 000(3/0) up to 7/0. • Use standard color coded wires to avoid confusion. – red: positive • Resistance – black: ground or common reference point – 22 gauge .0254 in 16 ohm/1000 feet – 12 gauge .08 in 1.5 ohm/1000 feet – Other colors: signals – High voltage AC used to reduce loss • Circuit flow, signal flow left to right • Higher voltage on top, ground negative voltage on • 1cm cube of copper has a resistance of 1.68 micro ohm (resistance of copper wire scales linearly : bottom length/area) • Neat wiring helps in debugging!

6.101 Spring 2020 25 6.101 Spring 2020 26

Wires Theory vs Reality ‐ Lab 1 Bypass (Decoupling) Capacitors

Electrolytic Bypass capacitor Capacitor 10uf 0.1uf typical

• Provides additional filtering from main power supply • Used as local energy source – provides peak current during 30-50mv voltage drop in chip transitions Wires have inductance and • Provided decoupling of resistance noise spikes during power transitions supply • Placed as close to the IC noise as possible. noise during transitions • Use small capacitors for Voltage drop across wires high frequency response. • Use large capacitors to LC ringing after transitions Through hole PCB (ancient) shown for clarity. localize bulk energy storage 6.101 Spring 2020 Lecture 2 27 6.101 Spring 2020 Lecture 2 28 Two of Many Methods of Modulation The Concept of Modulation (modulating a carrier)

x(t) Transmitted Signal

Carrier Signal Why? • More efficient to transmit E&M signals at higher frequencies. • Transmitting multiple signals through the same medium using different carriers. • Increase signal/noise ratio in lock‐in measurements. • others...

How? • Many methods Focus is on Amplitude Modulation (AM)

6.101 Spring 2020 Lecture 2 29 6.101 Spring 2020 30

Fourier Series

(n1) Time Domain Analysis 1  n ?  v  (Ac  KAm cosmt)*cosct T= 1/f1 KA  v  A cos t  m [cos(  )t  cos(  )t] c c 2 c m c m

V=|Asin(ω0t)| ω0 = 2π f1

6.101 Spring 2020 31 6.101 Spring 2020 Lecture 2 32 Amplitude Modulation (AM) of a Complex Asynchronous Demodulation Exponential Carrier • Assume c >> M, so signal envelope looks like x(t)

j c t • Add same carrier ct  e , c — carrier frequency j t y(t)  x(t) e c

1 Yj  Xj  Cj 2 1  Xj  2  Time Domain 2 c

Frequency Domain A + x(t) > 0 why?  Xj c

6.101 Spring 2020 Lecture 2 33 6.101 Spring 2020 34 Lecture 2

AM with Carrier (for different Amplitudes of A) Asynchronous Demodulation (continued) xm (t)  A c(t) D1 Envelop Detector

xm (t)

c(t) In order for it to function properly, the envelop function must be positive definite, i.e. A + x(t) > 0.

t Simple envelop detection for asynchronous demodulation. D1: 1N914 or 1N4148

y(t)  xm (t)c(t)

6.101 Spring 2020 35 6.101 Spring 2020 Lecture 2 36 Units Standard Values

6.101 Spring 2020 Lecture 2 37 6.101 Spring 2020 38

Diodes Finger Tips Facts

• Current thru pn junction doubles for every 26mv (at room temperature) or 10x for every 60mv

qvD kT I D  I s (e 1) • Temperature coefficient of silicon diode is ~2mv/degC at room temperature

• Small signal resistance of pn junction is kT/q is also known as the thermal voltage, V . T 1 ohm @26 ma, 26 ohm @1ma VT = 25.9 mV = ~ 26mv when T = 300K, room temperature.

6.101 Spring 2020 Lecture 2 39 6.101 Spring 2020 40 Diode V‐I Characteristic Reverse Breakdown Voltage

Low doped diodes have higher breakdown voltage qvD kT ID  Ise

kT thermal voltage q  26mv

Is 10pa

http://en.wikipedia.org/wiki/File:Diode_current_wiki.png

6.101 Spring 2020 Lecture 2 41 6.101 Spring 2020 Lecture 2 42

Zener Diode Zener Breakdown

4.7k • Actually caused by two effects: avalanche effect and zener effect.

• Avalanche effect: electron/holes entering depletion region is accelerating by the electric field, collides and creates additional + electron/hole pairs – like a snow avalanche; occurs above 5.6V; has positive temperature coefficient V _ • Zener effect: heavy doping of PN junction results in a thin depletion layer. Quantum tunneling results in current flow; • Zener diodes will maintain a occurs below 5.6V; has negative temperature coefficient fixed voltage by breaking down at a predefined voltage (zener • At 5.6V, two effects balance is near zero temperature voltage). coefficient.

6.101 Spring 2020 Lecture 2 43 6.101 Spring 2020 44 1N4001‐1N4007

6.101 Spring 2020 45 6.101 Spring 2020 46

Transient Respopnse Diodes Type Max Vr Max I Recovery Capaciitance Continous time 1N914 75V 10ma 4ns 1.3pf 1N4002 100V 1000ma 3500ns 15pf 1N5625 400 3000ma 40pf 1N1084 4000 30,000ma (peak) 400 50,000ma

Fast reverese recovery diode needed for switching power supplies

6.101 Spring 2020 Lecture 2 47 6.101 Spring 2020 Lecture 2 48 1N4001 Diode Circuits 1N914, 1N4148

1N7XX

Pulse Ox

Diode types

6.101 Spring 2020 Lecture 2 49 6.101 Spring 2020 Lecture 2 50

RC Equation More Diode Circuits

Vs = 5 V

Vs = 5 V Switch is closed t<0 Switch opens t>0 R Vs = VR + VC dV C c Vs = iR R+ Vc iR = dt dV + c t V = RC Vc    s dt Vc V  51 e RC  c   -   t    V  V 1 e RC  c s    

Is RC in units of time?

Lecture 2 6.101 Spring 2020 Lecture 2 51 6.101 Spring 2020 52 Clamping Circuit Light Emitting Diode

• LED’s are pn junction devices which emit light. The frequency of the light is determined by a combination of gallium, arsenic and phosphorus. • Red, yellow and green LED’s are in the lab • Diodes have polarity • Typical forward current 10‐20ma

RC time constant limitation

6.101 Spring 2020 Lecture 2 53 6.101 Lecture 2 54

Optical Isolators Pulse‐Oximetery

• Optical Isolators are used to • A non‐invasive photoplethysmographical (PPG) transmit information approach for measuring pulse rate and oxygen optically without physical saturation in blood. contact.

• Single package with LED and • Oximetry developed in 1972, by Takuo Aoyagi and photosensor (BJT, thyristor, Michio Kishi etc.) • Commercialized by Biox in 1981 and Nellcor in • Isolation up to 4000 Vrms 1983. • Used in pulse‐oximetry Nellcor DS-100 Pulse-ox

6.101 2020 Lecture 2 55 6.101 2016 Lecture 2 56 Pulse‐Oximetry Sensor Pulse‐Oximetry

• Two measurements: – Pulse rate finger – Oxygen saturation – Challenge: measuring 5‐20 nA!

• Heart rate easily accomplished with two IC’s!

Why plastic DB-9?

http://energymicroblog.files.wordpress.com/2012/11/figure-1.png

6.101 2016 Lecture 2 57 6.101 2016 Lecture 2 58

Reflective PPG* “Fitbit” Lab

*Fitbit Patent: US 2014/0275852 Wearable Heart Rate Monitor SFH 7050: 3 leds, 1 photodiode in one package

Lecture 2 60 Transimpedance Amplifier Transimpedance Amplifier (Current to Voltage Converter) (Current to Voltage Converter)

Ir Idiode

Ir = Ip 0.96V Vout

Vout = Ip Rf

At low frequency Vout  Idiode R3

9 6 Idiode  5x10 R3  4x10 V  20mv http://en.wikipedia.org/wiki/File:TIA_simple.svg out

Lecture 2 61 Lecture 2 62

“Fitbit” Lab Voltage

• What is the equation describing the voltage from a 120VAC outlet? • 120 VAC is the RMS (Root Mean Square Voltage) • 60 is the frequency in hz • Peak to peak voltage for 120VAC is 340 volts! 

negative battery terminal 120 2 sin 2 60t 169.7sin 2 60t

Virtual ground at 4.5V not shown 340 V

Lecture 2 63 6.101 Spring 2020 64 RMS Voltage RMS Derivation 

 v  Asin t • The RMS voltage for a sinusoid is that value v2  1 1  which will produce the same heating effect rms  v2dt  A2 sin 2 tdt (energy) as an equivalent DC voltage.    r r 0 r 0 vrms • Energy = 1  t 1  Pdt  vidt  v2dt sin 2dt   sin 2t t = π   [ ]0 0 r 0 0 2 4 • For DC, 2 vrms  2 2  vrms A t 1 i r  [  sin 2t ] • Equating and solving, A = 2 v 0 + rms r r 2 4 v - A = 2 vrms

6.101 Spring 2020 65 6.101 Spring 2020 66

Agilent Function Generator Agilent DMM

Turn on output!

6.101 Spring 2020 67 6.101 Spring 2020 68 Oscilloscope Controls Tektronix Oscilloscope

• Auto Set, soft menu keys • Signal measurement –time, • – frequency, Trigger – voltage – channel, –cursors – slope, – single sweep – Level

• Input • Image capture – AC, DC coupling, Data export Menu driven – 10x probe, soft key/buttons – 1khz calibration source, – probe calibration, – bandwidth filter

6.101 Spring 2020 69 70

Agilent Oscilloscope

Menu driven soft key/buttons