EE 105 | Discussion 3Kieran Peleaux & Qiutong Jin

Discussion Outline• HW3 | amplifier models & SPICE• Prelab 2 | VTC, offset voltage & input bias current• Review closed vs. open-loop gain• Gain error• Slew Rate

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HW3: Amplifier Models• Need to implement a nonideal op amp (finite gain & BW) in

SPICE• Use the standard amplifier model (be careful when choosing

values for 𝑅𝑅𝑖𝑖𝑖𝑖 and 𝑅𝑅𝑜𝑜𝑜𝑜𝑜𝑜!)• How to implement finite BW?

EE 105 | K. Peleaux & Q. Jin | Fall 2020 3

HW3: SPICE Netlists• Some notes on SPICE netlists

– For sources to be used for ac analysis use the syntax:vname vs gnd ac 1

– ac tells SPICE this is an ac source with magnitude indicated by following number

– Magnitude of 1 make 𝑣𝑣𝑜𝑜(𝑠𝑠)/𝑣𝑣𝑖𝑖 𝑠𝑠 = 𝑣𝑣𝑜𝑜 𝑠𝑠 (makes plotting simpler)– Remember to set your y-axis to db20 scale and your x-axis to log scale

in awaves– Remember, SPICE syntax is case-insensitive (one of the most common

errors is using the M prefix (interpreted as milli) rather than the megprefix (interpreted as mega)

– Units aren’t necessary– Nodes can have the same name as sources, but this isn’t recommended

(harder to tell what’s what)– 1st line is always a comment, last line must be .end– For more comments, begin line with *

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Prelab 2: Amplifier VTC• Describes relationship between input and output of amplifiers• What can we learn from VTC?

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EE 105 | A. Ameri & K. Peleaux | Fall 2019 6

Recall our qualitative understanding for why 𝑣𝑣+ = 𝑣𝑣− when 𝐴𝐴𝑜𝑜 = ∞→ In actuality, setting both 𝑣𝑣+& 𝑣𝑣− = 0 will result in a nonzero 𝑣𝑣𝑜𝑜→ This is due to mismatches in the op amp differential pair (we’ll see this later)

Ideal op ampNonideal op amp

Nonideal Op Amps | Offset Voltage

𝑣𝑣+

𝑣𝑣𝑜𝑜

𝑣𝑣−

𝑉𝑉𝑜𝑜𝑜𝑜

Prelab 2 | Input Offset Voltage• What is this circuit doing?

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EE 105 | A. Ameri & K. Peleaux | Fall 2019 8

If 𝑖𝑖+, 𝑖𝑖− ≠ 0, what’s another way to describe this nonideality?

Ideal op ampNonideal op amp

Nonideal Op Amps | Input Bias Current

𝑣𝑣+

𝑣𝑣𝑜𝑜

𝑣𝑣−

𝐼𝐼𝑏𝑏𝑖𝑖𝑏𝑏𝑜𝑜

𝐼𝐼𝑏𝑏𝑖𝑖𝑏𝑏𝑜𝑜

Prelab 2 | Input Bias Current• How can we separate offset voltage effects from input bias

current effects?

EE 105 | K. Peleaux & Q. Jin | Fall 2020 9

10 MΩ

Nonideal Op Amps | Finite Gain & Bandwidth

• Op amps without any feedback have open-loop gain 𝐴𝐴𝑜𝑜(𝑠𝑠)

𝐴𝐴𝑜𝑜(𝑠𝑠) =𝐴𝐴𝑜𝑜

1 + 𝑠𝑠𝜔𝜔𝑏𝑏

EE 105 | A. Ameri & K. Peleaux | Fall 2019 10

Nonideal Op Amps | Finite Gain & Bandwidth

• At DC, 𝐴𝐴𝑜𝑜(𝑠𝑠) = 𝐴𝐴𝑜𝑜, which is finite in real op amps• When we close the loop, this results in a deviation from the

expected gain

EE 105 | A. Ameri & K. Peleaux | Fall 2019 11

Define gain error, 𝜖𝜖 = 𝐴𝐴𝑣𝑣,𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 −𝐴𝐴𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎0𝐴𝐴𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖𝑎𝑎𝑎𝑎

× 100

Nonideal Op Amps | Finite Gain & Bandwidth

EE 105 | A. Ameri & K. Peleaux | Fall 2019 12

𝜖𝜖 =𝐴𝐴𝑣𝑣,𝑏𝑏𝑎𝑎𝑜𝑜𝑜𝑜𝑏𝑏𝑎𝑎 − 𝐴𝐴𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖𝑏𝑏𝑎𝑎

𝐴𝐴𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖𝑏𝑏𝑎𝑎× 100

Nonideal Op Amps | Slew Rate

Slew rate (SR) refers to the max rate of change of an amplifier’s output voltage

𝑆𝑆𝑅𝑅 ≜ �𝑑𝑑𝑣𝑣𝑜𝑜𝑑𝑑𝑑𝑑 𝑚𝑚𝑏𝑏𝑚𝑚

This imposes two limitations on the output1. Amplitude (i.e. Δ𝑉𝑉𝑜𝑜) → Δ𝑉𝑉𝑜𝑜 ≤ 𝑆𝑆𝑅𝑅 ⋅ Δ𝑑𝑑

2. Frequency (i.e. Δ𝑑𝑑) → Δ𝑑𝑑 ≥ Δ𝑉𝑉𝑜𝑜𝑆𝑆𝑆𝑆

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Nonideal Op Amps | Slew Rate

EE 105 | A. Ameri & K. Peleaux | Fall 2019 14

Input voltage step

Output voltage waveform, SR-limited Output voltage waveform, not SR-limited

Unity-gain bufferLimitation #1: Amplitude (i.e. Δ𝑉𝑉𝑜𝑜)

Δ𝑉𝑉𝑜𝑜 ≤ 𝑆𝑆𝑅𝑅 ⋅ Δ𝑑𝑑

Nonideal Op Amps | Slew Rate

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𝑣𝑣𝑜𝑜 𝑑𝑑

Limitation #2: Frequency (i.e. Δ𝑑𝑑) → Δ𝑑𝑑 ≥ Δ𝑉𝑉𝑜𝑜𝑆𝑆𝑆𝑆

Sinusoidal output waveform, SR-limited