1. Intro to Analog & Audio Electronics
IEEE CONCORDIA: Intro to analog and audio electronics
Intro to Analog & Audio Electronics
The op-amp in practical analog design
Marc-Alexandre Chan Nathaly Arraiz
Eric Tremblay Michael Levan
IEEE Concordia 11 April 2015
Image source: Rebecca Wilson (Flickr: Vicariously). CC-BY-2.0.
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2. Why analog? Digital is taking over the world But the world is analog
Easier, more predictable, less prone to noise
But the world is analog
Sensors: acceleration, temperature, light, EEGs, …, plant resistance ;)
Communication via radio waves and voltage waves
Need analog to interface world with digital: need to drive ADCs and DACs
Because analog is fun!
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3. Expected background This workshop is practical. Math is at a minimum!
ELEC273 (or the EMAC electronics crash course!)
ELEC264 and 364 useful but not necessary
The nature of current and voltage
Ohm’s law, Thévenin/Norton equivalent circuits
Frequency response, impedances
Basic op-amps
This workshop is practical. Math is at a minimum!
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4. What will we learn? A taste of large variety of op-amp circuits
How those circuits work
Intuition is important! No long mathematical derivations!
How small building blocks make up a big circuit
How to build & debug circuits on a breadboard
Make an audio project!
Simple 2-channel mixer
Synth modules: voltage-controlled oscillator & amplifier
Make your own!
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5. What will we learn? Op-amp basics (make big signals!)
Filters I (how to play with frequencies)
MAKE: Audio mixer! (Cute little two-channel console!)
Break for food
Interlude: Non-Ideal Op-Amp (Enough with the fantasies!)
Filters II: higher-order filters and tone control
Non-linear op-amp circuits II (ooh, voltage control)
MAKE: Synth! Activity LED!
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6. 1 A Review of the Ideal Op-Amp
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7. 1 Why op-amps?
Op-amps are the “bread and butter” of board-level analog
Integrated circuits (ICs) are transistors made from silicon
Inside more complicated ICs, it’s common to “copy-paste” an op- amp transistor circuit!
Incredibly versatile!
Negative feedback gives a lot of control on circuit behaviour (but sometimes very complex)
Fig. 1 DIP integrated circuit, 14-pin. Op-amps come in a variety of packages used for integrated circuits, like DIPs.
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8. 1 What is an op-amp? Amplifier: makes voltages bigger!
Input voltage is difference between the two inputs
“differential mode” input
Gain is “infinite”! (Actually 100,000 to 1,000,000)
Input differential voltage multiplied by “infinity” on output!
Negative feedback to control gain < infinity
With large gain + negative feedback, op-amp tries to keep the two inputs almost equal!
Fig. 2 Op-amp symbol, with labelled pins.
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9. 1 What is an op-amp? Basic limitations
Op-amps have gain-bandwidth (GBW)
GBW = gain x bandwidth
Means you have a limitation on frequency at specific gain
GBW of 1MHz to 50MHz common; higher is expensive
Output cannot go beyond power supplies
“General-purpose” op-amp: if ±5 V supplies, ±4 V out?
“Rail-to-rail” op-amp: can go within mV of supplies
Bipolar (±) v. single supply
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10. 2 Basic amplifiers
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11. 2 Basics: Voltage follower
a.k.a. unity buffer
Outputs the same voltage as the input
Why?
Maybe Vin has a high output resistance? Op-amp has low output resistance and can provide more current.
Maybe you need to provide a lot of current to whatever you connect this to? Use a high-current op-amp.
Fig. 3 Voltage follower schematic.
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12. 2 Basics: Non-inverting amplifier
Makes voltages bigger!
Gain = (1 + Rf / R1) V/V
How to choose R?
Small = lots of current = power waste + heat
Big = more noise (thermal + electromagnetic waves in the air)
10 kΩ to 1 MΩ often a good start
Fig. 4 non-inverting amplifier schematic.
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13. 2 Basics: Non-inverting amplifier
Try it!
But first… how the heck do you connect a circuit together?
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14. 2 Breadboard Breadboard: Making connections without a mess!
No solder, no PCB design, no chemicals
Good for quick low-frequency prototyping
In Figure: green = the pattern of connected holes
Tip: insert leads straight downward with even, steady pressure, one at a time. Otherwise your leads will bend or break!
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15. 2 Breadboard
Fig. 5 Breadboard diagram. (Source: Nevit Dilmen, Wikimedia Commons)
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16. 2 The NE5532 op-amp We are using the NE5532 op-amp
Two op-amps in one chip
10MHz GBW (pretty good), very low noise (req for audio!)
“general purpose” chip (not rail-to-rail)
All technical info in datasheet:
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17. 2 The NE5532 op-amp
Fig. 6 NE5532 pinout. (Source: TI, NE5532 datasheet)
Fig. 7 Mapping of NE5532 pins to op-amp symbol.
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18. 2 Basics: Non-inverting amplifier
Try it!
Rf = 33k
R1 = 10k
𝑉 𝑜𝑢𝑡 =2 𝑉 𝑖𝑛 (or +6dB)
Test it: put a pot at Vin to control input voltage -5 to 5V. Use a multimeter at the output.
Test it: try your phone/MP3 player at low volume! Compare with/without amplifier.
Fig. 7 Non-inverting amplifier schematic.
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19. 2 Basics: inverting amplifier
Similar to non-inverting
Switch ground and Vin around!
Flips signals upside-down
Warning:
always use Rf ≥ Rin
Gain < 1 is not stable (oscillates)
Why?
More flexible for later circuits; single-supply design.
Why not?
Mixing (adding) inverted and non-inverted signals = signals cancel out!
Fig. 8 Inverting amplifier schematic.
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20. 2 Basics: inverting w/attenuation
Gain < 1 not stable … how can we do it?
Add a voltage divider or potentiometer in front
Volume control!
Fig. 9 Inverting amplifier with attenuation.
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21. 2 Basics: Summing amplifier
Add signals together
Audio mixers are based on this at the core
Can add V3-R3, V4-R4, etc. to add more signals
R1, R2, etc. sets the “weight” of each input
Fig. 10 Summing amplifier.
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22. 2 Basics: Difference amplifier
Takes the difference between two voltages (each multiplied by a constant).
If R3 = R4 and R1 = R2,
𝑉 𝑜𝑢𝑡 = 𝑅 3 𝑅 1 𝑉 2 − 𝑉 1
Fig. 11 Difference amplifier.
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23. 2 MAKE: Core audio mixer Faders for volume control (–∞dB to +13.5dB)
Faders are logarithmic, not linear: put them in the right way!
Use low volume on phone/MP3 player: let the circuit do the amplification!
Fig. 12 Core audio mixer with fader volume/gain control.
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24. 3 Basic Filters
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25. 3 Filters: Frequency domain
Signals made up of a “sum of sines”
Each sine is at some different frequency
Fourier series and Fourier transform to decompose them
Periodic signals: concept of “harmonics”
Circuits that respond differently to different frequencies
Capacitors, inductors are like frequency- dependent resistors (plus a phase shift)
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26. 3 Filters: Frequency domain
Fig. 13 Square wave with first four harmonics (sine wave components). We can see the wave slowly approaching the ideal square wave as more harmonics are added.
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27. 3 Filters: Frequency response
Circuits that act differently (different gain, etc.) according to the input frequency
In a signal with many frequencies, acts on each frequency separately
Example: low-pass filter with 20dB passband gain
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28. 3 Filters: Lowpass RC filter
Passive filters made of only RLC, no amplifiers
With R1-R2 series, voltage division: 𝑉 𝑜𝑢𝑡 = 𝑅 2 𝑅 1 + 𝑅 2 𝑉 𝑖𝑛
But R2  C2, C is like a frequency-dependent R
Impedance of C: Z C = 1 2𝜋𝑓𝐶 𝑉 𝑜𝑢𝑡 = 𝑉 𝑖 𝑍 𝐶 𝑍 𝐶 + 𝑍 𝑅
Vout
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29. 3 Filters: Highpass RC filter
Lowpass: blocks frequencies above corner frequency
Highpass: blocks frequencies BELOW corner frequency (including DC)
Same impedance/voltage division concept
𝑓 𝑐 = 1 2𝜋𝑅𝐶 is the corner frequency for both filters.
Vout
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30. 3 Filters: RC filters How to design RC circuits?
Choose desired corner frequency fc
Choose a reasonable C first
Fewer available values than R (10, 15, 33, 47 common)
Not too big (>1μF: expensive OR imprecise, not good for filters!)
Not too small (<100pF: parasitic capacitance creates error in fc)
Then choose R (isolate it in fc equation)
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31. 3 Filters: Active (amplified)
Passive problems
Load impedance
Vout ≤ Vin
1st order active lowpass
RC + amplifier
High input Z, low output Z
Analytic equations:
Gain: 𝑉 𝑜 𝑉 𝑖 =1+ 𝑅 2 𝑅 1 at low frequency (amplifier)
Corner freq: 𝑓 𝑐 = 1 2𝜋 𝑅 3 𝐶 1 (RC filter)
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32. 3 Filters: Active (amplified)
1st order lowpass inverting
Good (with small modification) for single supply circuits
+ terminal to ground  virtual ground at – terminal
Filter happens in feedback loop
Analytic equations:
Gain: 𝐴 𝑣0 =− 𝑅 2 𝑅 1 at low frequencies
Corner: 𝑓 𝑐 = 1 2𝜋 𝑅 2 𝐶
Design: Choose fc and Av0. Pick a reasonable C. Solve for R2 in fc eqn. Solve for R1 in Av0 eqn.
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33. 3 Filters: MAKE! Play some music and hear the filtering!
Try passive RC and non-inverting RC if you want.
1st order active inverting lowpass filter.
Analytic equations:
Gain: 𝐴 𝑣0 =− 𝑅 2 𝑅 1
Corner: 𝑓 𝑐 = 1 2𝜋 𝑅 2 𝐶
Try this design:
𝑓 𝑐 =3.3 kHz, 𝐴 𝑣0 =−2, 𝐶=4.7 nF
Solve for 𝑅 2 = 1 2𝜋 𝑓 𝑐 𝐶 ≈10 kΩ
Solve for 𝑅 1 =− 𝑅 2 𝐴 𝑣0 =5 kΩ
Play some music and hear the filtering!
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34. 4 MAKE! Simple mixer!
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35. IEEE CONCORDIA: Intro to analog and audio electronics
4 MAKE!: Simple Mixer
Notes:
Summing amp has 2 input channels. You can add more.
Usually the LPF would be a 3-band EQ at the input of each channel. We use an LPF for simplicity: EQ is complex!
See how we took building blocks to make a bigger circuit? This is how complex circuits are made! Σ
Music Input
Faders
Summing Amp
1stO active invert. LPF
Speaker

36. 5 Food!
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37. 6 Interlude
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38. 6 Why “ideal” op-amp? Do we really have infinite gain?
No: usually 100,000x to 1,000,000x.
Infinite gain desired: with negative feedback and infinite gain, op-amp changes output to keep both inputs equal!
Are there other limitations to ideal op-amps?
Many!
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39. 6 Non-ideal op-amp: a summary
Real op-amp design can be complicated.
Op-amps act like a low-pass filter
Has a max frequency (“bandwidth”).
This max frequency is called bandwidth.
More closed-loop gain = less bandwidth.
GBW (gain x bandwidth) is constant.
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40. 6 Non-ideal op-amp: a summary
Output voltage is limited.
Cannot go beyond power supply voltages, often less.
“General purpose”: ±5V supply, maybe only ±4V output!
“Rail-to-rail”: ±5V supply, maybe ±4.9V output: better!
Single supply design
It’s hard to make ± power supplies: single voltage easier!
Inverting amplifiers have + pin direct to ground. Can use voltage divider there to add a DC offset: for example, use +5V supply and center all signals at 2.5V.
Can’t do this with non-inverting: impedance problems with a voltage divider. Need to make a low-Z virtual ground.
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41. 6 Non-ideal op-amp: a summary
Stability
Op-amp circuit can oscillate or ring (bad oscillations that die down).
Solution:
Increase gain of circuit
Reduce bandwidth with cap (make low-pass)
Use capacitor elsewhere for stability compensation (e.g. in parallel to a feedback resistor of non-inverting amp)
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42. 6 Non-ideal op-amp: a summary
Noise on power supply can appear on signal
e.g. 60 Hz hum
Solution: capacitor to ground near every chip. 1μF to 0.01μF ceramic common (try 0.1μF).
This is called decoupling.
In a real circuit: always do this for every chip!
Op-amp inherently generates its own noise: for audio, look for < 10 nV/√Hz
Fig. An op-amp showing its decoupling capacitors. If this were single supply (only +5V and 0V, no negative), then only C1 would be necessary.
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43. 6 Non-ideal op-amp: a summary
DC offset
Small current (1pA to 1μA) into input pins
Op-amp inherently has an output voltage for 0 input
Both cause DC offset to appear on the output
Solution: Some chips have offset trim. Some circuits let you use a pot to adjust offset. Chopper amplifier auto- cancels its own DC offset.
Solution 2: Use a capacitor IN SERIES to remove DC offset from signal and only let AC through. Very common in audio (try 470μF). This is called AC coupling.
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44. 6 Non-ideal op-amp: a summary
Capacitors: not all equal!
“Metal can” (aluminium electrolytic) caps are very bad for precise filters (precision: +50% to –20%!)
“Metal can” very good for power supply noise filter (very big C value)
For filters with precise cutoff frequency, use:
Ceramic disk capacitors: cheap but ±5% easy to find! ≤1μF
Some film capacitors are more precise/temperature-stable/etc.
Silver mica: huge and expensive, but incredibly precise. Great for precision RF circuits: e.g. high-Q bandpass filter.
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45. 6 Non-ideal op-amp: a summary
Stability
Op-amp circuit can oscillate or ring (bad oscillations that die down).
Solution:
Increase gain of circuit
Reduce bandwidth with cap (make low-pass)
Use capacitor elsewhere for stability compensation (e.g. in parallel to a feedback resistor of non-inverting amp)
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46. 7 Higher order filters
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47. 7 Higher order filters 1st order filter (seen before)
At frequencies higher than fc, gain decreases at 20 dB/decade (6 dB/octave).
Higher-order filters = more parts but better cutoff (20×(order) dB/decade)
Easier to cut out frequencies you don’t want
Resonance = tone control! (Usually lowpass.)
We will look at 2nd order filters
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48. 7 Second order filter Tone control = quality factor control
Q = 1 2𝜁 , 𝜁 is the damping ratio (ELEC364/372)
Overdamped/critically damped
Q < 0.5, Q = 0.5. Boring, flat frequency response.
Underdamped
Q > 0.5. Enhances a narrow range of frequencies: adds tonal colour to sound depending on the frequency!
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49. 7 Second order filter
Fig. Frequency response of various second-order filters, with the same resonant frequency but different Q factors (damping factors). We can see the peak characteristic of underdamped filters.
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50. 7 Sallen-Key Filter Simple second-order lowpass filter circuit
Unity gain version
For stability, gain A ≤ 3
𝐴=3− 1 𝑄
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51. IEEE CONCORDIA: Intro to analog and audio electronics
7 Sallen-Key Filter
Example: simplify 𝑅 1 = 𝑅 2 , 𝐶 1 = 𝐶 2
What does that do to Q?
Example:
𝑓 𝑐 =5 kHz, 𝑄=3,𝐶=33 nF
𝐴=3− 1 3 =2.67
𝑅 𝐴 𝑅 𝐵 =1.67 → 𝑅 𝐴 =5 kΩ, 𝑅 𝐵 =3 kΩ
To vary 𝑓 𝐶 & 𝑄, make R1/R2 variable
Not good tone control: 𝑓 𝐶 & 𝑄 both vary with each of R1 and R2
But a simple circuit to start with!
Tow-Thomas biquad gives good control!
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52. 8 Non-Linear Circuits
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53. 8 NL: Comparator Open circuit opamp = comparator
If V2 > V1, Vo = 5V
If V2 < V1, Vo = 0V
Notice that opamp changed (MCP6004)
This is a rail-to-rail op-amp
The power supplies are 5V and ground too
Not the best comparator: opamps are slower than dedicated comparator chips
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54. 8 NL: Schmitt trigger V1 DC and noisy V2: what happens?
Comparator output turns on and off due to noise crossing the V1 threshold several times
We can add “dead zone” bigger than noise to prevent this
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55. 8 NL: Schmitt trigger
𝑉 𝑡ℎ𝑟,ℎ𝑖𝑔ℎ = 𝑅 𝑖𝑛 𝑅 𝑓 +1 𝑉 𝑟𝑒𝑓 + 𝑉 𝑜,𝑚𝑖𝑛 𝑅 𝑖𝑛 𝑅 𝑓
𝑉 𝑡ℎ𝑟,𝑙𝑜𝑤 = 𝑅 𝑖𝑛 𝑅 𝑓 +1 𝑉 𝑟𝑒𝑓 − 𝑉 𝑜,𝑚𝑎𝑥 𝑅 𝑖𝑛 𝑅 𝑓
If 𝑉 𝑖𝑛 > 𝑉 𝑡ℎ𝑟,ℎ𝑖𝑔ℎ , 𝑉 𝑜 = 𝑉 𝑜,max
If 𝑉 𝑖𝑛 > 𝑉 𝑡ℎ𝑟,𝑙𝑜𝑤 , 𝑉 𝑜 = 𝑉 𝑜,m𝑖𝑛
If 𝑉 𝑖𝑛 in between, 𝑉 𝑜 keeps its old value
In this circuit: max/min = 5V/0
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56. 8 NL: Precision rectifier
Recall: half-wave rectifier
Precision rectifier
Acts like ideal diode (no diode drop)
Only positive voltage passes
Current flows when Vin > 0
Open loop when Vin < 0
Vin = Vout
Vin,max = Vout,max = VDD – Vdiode
RL necessary to make sure “enough” current can flow through D1
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57. 8 NL: Peak or volume detector
Precision rectifier stores max value of Vin on C1
When Vin is increasing, current from op-amp+D1 charges C1, so Vout = Vin
When Vin is decreasing, C1 holds the max value of Vin … but R1 discharges C1 so Vout decreases
Choose R1-C1 so that discharge is fast enough to capture volume reduction, slow enough to really get the volume envelope and not the audio part of the waveform.
Time constant τ = R1C1
MCP6004
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58. 8 NL: Voltage-ctrl. current source
Two versions: “sink” and “source” current
Idea: negative feedback so V+ = V- of opamp.
But V- is also voltage of Rs: this sets 𝐼 𝑅𝑠 = 𝑉 − 𝑅 𝑠
M1 transistor limits current depending on opamp output (don’t care about equations, opamp regulates it)
Can be used to control LED brightness (analog, no digital PWM!) or other constant-current things
𝐼 𝑜 = 𝑉 𝑐𝑡𝑙 𝑅 𝑠
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59. 8 NL: Voltage-ctrl. current source
Circuit has Vctl/Io limits because op-amp output has limits
If rail-to-rail op-amp:
𝐼 𝑜 = 𝑉 𝑐𝑡𝑙 𝑅 𝑠
𝑉 𝑐𝑡𝑙,𝑚𝑖𝑛 =0𝑉
→ 𝐼 𝑜,𝑚𝑖𝑛 =0𝐴
𝑉 𝑐𝑡𝑙,𝑚𝑎𝑥 ≈ 𝑉 𝐷𝐷 − 𝑉 𝑡ℎ,𝑀1 − 2 𝑉 𝐷𝐷 − 𝑉 𝑡ℎ,𝑀1 𝐾 𝑀1 𝑅 𝑠
𝐼 𝑜,𝑚𝑎𝑥 ≈ 𝑉 𝐷𝐷 − 𝑉 𝑡ℎ,𝑀1 𝑅 𝑠 if 𝑅 𝑠 ≫1
𝑉 𝑡ℎ,𝑀1 is M1’s threshold voltage
𝐾 𝑀1 = 𝜇 𝑛 𝐶 𝑜𝑥 𝑊/𝐿 is M1’s transconductance
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60. 8 NL: Voltage-ctrl. current source
Current sourcing version
Same idea
𝐼 𝑜 = 𝑉 𝐷𝐷 − 𝑉 𝑐𝑡𝑙 𝑅 𝑠
𝑉 𝑐𝑡𝑙,𝑚𝑎𝑥 = 𝑉 𝐷𝐷 → 𝐼 𝑜,𝑚𝑖𝑛 =0𝐴
𝑉 𝑐𝑡𝑙,𝑚𝑖𝑛 ≈ 𝑉 𝑡ℎ,𝑀 𝑉 𝐷𝐷 − 𝑉 𝑡ℎ,𝑀2 𝐾 𝑀2 𝑅 𝑠
𝐼 𝑜,𝑚𝑎𝑥 ≈ 𝑉 𝐷𝐷 − 𝑉 𝑡ℎ,𝑀2 𝑅 𝑠 if 𝑅 𝑠 ≫1
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61. 9 NL: Voltage controlled amplifier
Idea: Use JFET as a voltage-controlled resistor TO GROUND in a normal amplifier.
Voltage across JFET should be small for it to act as a resistor: amplify AFTER.
Didn’t have time to design!
/analog/op-amp-and-two- jfets-form-voltage- controlled-amplifier
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62. 9 MAKE! Advanced!
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63. 9 MAKE! Channel activity LED
Concept: detect volume and modulate LED brightness according to volume
Use on mixers to show whether a channel has any activity or not.
D1 = 1N4148
C1 = 100 nF
R1 = 470 kΩ
Rs = 200 Ω ( )
From mixer
MCP6004
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64. 9 MAKE! Voltage ctrl. oscillator
Awesome circuit to demonstrate design of a more complicated circuit!
Interested? Confident? Talk to Marc for a design walkthrough!
Outputs triangle (±0.5V) and square wave (±4V)
f = Hz to 1.25 KHz (~3.5 octaves)
𝑓 𝑜𝑢𝑡 = 𝐻𝑧 𝑉 𝑉 𝑐𝑡𝑙 𝐻𝑧
Improvement: add exponential converter (BJT circuit) to get V/octave control instead of V/Hz
Use mixer with two outputs, or add a tone control, or add a voltage-controlled amplifier …!
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65. 9 MAKE! Voltage ctrl. oscillator
VDD
U1A Σ∫
VCH
Summing Integrator
U2A
VDD
U1B ∬ -Σ
Schmitt Comparator
Summing Inverter
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66. 9 MAKE! Voltage ctrl. oscillator
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67. 9 MAKE! Synth module
Put both oscillator outputs into the summing amp: you can play with combining the two waveforms together! Σ
Oscillator
Faders
Summing Amp
Tone Control
Speaker
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68. What next? Want to make a mixer? Modular synth?
Add output volume control, sends, etc.
Learn how to do 3-band Eqing. Easy start: shelf filters.
Modular synth?
Very complex: filters & oscillators.
Voltage controlled amplifier: super important!
Learn about operational transconductance amplifiers. Very useful for voltage-controlled anything.
Envelope generator
Exponential converter (we hear volume & frequency logarithmically)
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69. What next? Guitar pedals? Learn transistor amplifiers! Other stuff?
Analog PWM generators
Radio transmitters/receivers
Communication circuits in general
Biomedical sensors (or any sensor that doesn’t already convert to digital!)
Analog control systems (power electronics, etc.)
And so much more!
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70. Thanks for coming!
Intro to Analog & Audio Electronics: The Op-Amp in Practical Analog Design 11 April 2015 Coordinated by Marc-Alexandre Chan With contribution of Nathaly Arraiz Matute Eric Tremblay and Michael Levan. Thanks to the IEEE Concordia exec team and the Electronic Music Association of Concordia for co-hosting this workshop!
Help make our tutorials better! Fill out the survey!
Questions? Want to know more? Head filled with project ideas? Stop by the lab to talk with us or work on your projects! See our office hours on the website or us.
IEEE Concordia Bishop Street, Room B-204 Montreal, Québec, Canada
Phone: ext Web:
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71. Appendices
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72. A. Further Reading
W. Storr. (2015). Electronics Tutorials [Online].
Op Amps for Everyone,“Active Filter Design Techniques”, Texas Instruments, 2008, pp Available
Excellent book for the more engineering oriented! Good discussions on op-amps and other kinds of amplifier chips, and in-depth talk about design of op-amp circuits. It does assume knowledge of circuit analysis, stability (phase/gain margin, open v. closed loop transfer functions, etc.), etc.
Application Report, “Analysis of Sallen Key-Topology”, Texas Instruments, Available:
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