Announcements

1. Announcements • Assignment 5 due tomorrow (or now) • Project ideas due Nov 1st. (email 1 paragraph, plus web links) • No new assignment this week. Revise! • Mid-term next Thursday (27th) • Go through the Lectures, Assignments and Solutions • Use EWB to create test problems • Google “circuit analysis problems”!

3. Lecture 14 • Real world op amps • Op amp Slew Rate • Introduction to digital signals • Number codes • Digitization

4. Non-Ideal Opamps: Basic Cautions • 1) Avoid Saturation • Voltage limits: VS-< vOUT < VS+ • In the saturation state, Golden Rules of opamp are not valid

5. Basic Cautions for opamp circuits • 2) Feedback must be negative (inverting) for linear behaviour • 3) There must always be negative feedback at DC (i.e. when ω=0). • Otherwise any small DC offset will send the opamp into saturation • Recall the integrator: In practice, a high-resistance resistor should be added in parallel with the capacitor to ensure feedback under DC, when the capacitive impedance is high 4) Don't exceed the maximum differential voltage limit on the inputs: this can destroy the opamp

6. Frequency response limits • An ideal opamp has open-loop (no feedback) gain A= • More realistically, it is typically ~105-106 at DC, dropping to 1 at frequency, fT=1-10 MHz • The opamp also introduces a phase shift between input and output • At high frequencies, as the open-loop gain approaches 1, the phase shift increases • If it reaches >180º degrees, and the open loop gain is >1, this results in positive feedback and high frequency oscillations • The term "phase margin" refers to the difference between the phase shift at the frequency where the gain=1 (fT) and 180º

7. Frequency response limits • Open loop cut-off frequency, f0 (also known as open loop bandwidth) is usually small (typically 100Hz) to ensure that the gain is <1 at a phase shift of 180º • Closed-loop gain (gain of amplifier with feedback) begins dropping when open loop gain approaches RF/RS (in the case of the inverting amp) • Cut off frequency will be higher for lower closed-loop gain circuits Inverting amplifier

8. Slew rate (or rise time) • The maximum rate of change of the output of an opamp is known as the slew rate (in units of V/s) square wave input • The slew rate affects all signals - not just square waves • For example, at high enough frequencies, a sine wave input is converted to a triangular wave output due to limited slew rate

9. Slew rate example • Consider an inverting amplifier, gain=10, built using an opamp with a slew rate of S0=1V/μs. • Input a sinusoid with an amplitude of Vi=1V and a frequency, ω. • For a sinusoid, the slew rate limit is of the form AViω<S0. • We can therefore avoid this non-linear behaviour by • decreasing the frequency (ω) • lowering the Amplifier gain (A) • lower the input signal amplitude (Vi) • Typical values: 741C: 0.5V/μs, LF356: 50V/ μs, LH0063C: 6000V/ μs,

10. Op Amp Slew rate (or rise time) • The maximum rate of change of the output of an opamp is known as the slew rate (in units of V/s) square wave input • The slew rate affects all signals - not just square waves • For example, at high enough frequencies, a sine wave input is converted to a triangular wave output due to limited slew rate

11. Slew rate example • Consider an inverting amplifier, gain A=10, built using an opamp with a slew rate of S0=1V/μs. • Input a sinusoid with an amplitude of Vi=1V and a frequency, ω. • For a sinusoid, the slew rate limit is of the form AViω<S0. • We can therefore avoid this non-linear behaviour by • decreasing the frequency (ω) • lowering the Amplifier gain (A) • lower the input signal amplitude (Vi) • Typical values: 741C: 0.5V/μs, LF356: 50V/ μs, LH0063C: 6000V/ μs,

12. Stop Revising Here Stop Revising Here Stop Revising Here

13. Digital Electronics • Some simple concepts to begin with • Question: Why do we use digital electronics? • Allows transmission of analog signals (data) without degradation • Allows easy storage of data • Allows to perform calculations on the data

14. Why use digital circuits? • Digital signals, represented by ones and zeros, are very easy to handle with electronic circuits. • Only 2 states are required, e.g: • Switch ON or OFF • Circuit CLOSED or OPEN • Current FLOWING or NOT • Voltage HIGH or LOW • This leads to a low error rate - compare the accurate measurement of voltage required in an analog circuit to the requirement in digital, which is typically 0V-2V=0, 2.6V-5V=1

15. How can digital help? • Any numbers, letters and symbols can be represented using multiple binary digits • e.g. binary 101=5 • If we first digitize the analog signal, we only need transmit a stream of 1's and 0's

16. Digital system So, Ideally: What happens now when we add noise?

17. Digital system • So , the digital signal has better noise immunity • Lots of "noise margin" • For "1": noise margin is 5V to 2.5V=2.5V • For "0": noise margin is 0V to 2.5V=2.5V • Only true if sender sends 5V or 0V

18. What happens at 2.5V? • The digital state is unclear • Resolve this by creating a "no man’s land" or forbidden region where the signal is not valid e.g:

19. Helps a bit… but we can do better. If the sender sends a high state (1) = VOH or a low state (0) =VOL Input voltage to receiver must allow for possible noise contamination Little or no noise on the output voltage from sender It makes sense to have different thresholds for input and output voltage levels: High state ("1") noise margin is: VIH-VOH Low state ("0") noise margin is: VIL-VOL

20. What is the noise margin? So : The input high threshold is lower than the output high threshold The input low threshold is higher than the output low threshold Digital systems follow a discipline: If inputs to the system meet the valid input thresholds, the system guarantees that its outputs will meet the valid output thresholds e.g. TTL output: LOW<0.4V, HIGH>2.4V TTL input: LOW < 0.8V, HIGH > 2.0V 0.4V noise margin

21. How do we represent analog as digital?

22. Number codes: How to count! Decimal counting: each column is a power of ten Power of 10: 3 2 1 0 Weight: 1000 100 10 1 103 102 101 100 requires 10 symbols: 0,1,2,3,4,5,6,7,8 and 9 Example: 1998 = (1*103) + (9*102) + (9*101) + (8*100) = 1000 + 900 + 90 + 8

23. Binary Counting Binary counting: each column is a power of two Power of two: 7 6 5 4 3 2 1 0 Weight: 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 requires 2 symbols: 0 and 1 Example: Convert 1100010 to decimal Binary: 0 1 1 0 0 0 1 0 Weight:128 64 32 16 8 4 2 1 64 + 32 + 2 = 98

24. Definitions • 1 binary digit is a "bit". • 8 bits are a "byte” (B) • 1kB = 210 B = 1024 B • 1MB = 210 kB = 220 B = 1,048,576 B • More than 8 bits are a "word" (no fixed size – depends on architecture: Intel 8086 used 16 bit words, modern 32 or 64 bit processors keep this definition) • "Least significant bit" refers to the rightmost bit ( the 20 position) • "Most significant bit" refers to the leftmost bit (e.g. the 27 position in a byte)

25. Algorithm to convert decimal to binary Easy - divide by two and write down the remainder e.g. decimal 23 23 divide by 2 = 11 remainder 1 11 divide by 2 = 5 remainder 1 5 divide by 2 = 2 remainder 1 2 divide by 2 = 1 remainder 0 1 divide by 2 = 0 remainder 1 so 23 decimal is binary 10111 Convert 15710 to binary Answer:10011101

26. Addition of binary numbers 1 + 0 = 1 1 + 1 = 10 Don't forget to carry! 1 + 1 + 1 = 11 Which of the following is not true? A: 10 + 10 = 110 B: 11 + 11 = 110 C: 101 + 1 = 110 Answer: A (=100)