AMME1705 · Introduction to Electromechanical Systems
Op-Amps: Comparators & Amplifiers
Operational amplifiers are the analog signal-conditioning block at the heart of AMME1705 Introduction to Electromechanical Systems at the University of Sydney. This chapter shows how the two op-amp golden rules unlock every configuration you are examined on — the open-loop comparator, the inverting and non-inverting amplifiers, and the difference amplifier — plus saturation and the high-impedance-in / low-impedance-out behaviour that makes an op-amp a buffer. Everything is worked from first principles with SI units so a resistor ratio, a sign, or a rail never trips you up.
What this chapter covers
- 01State the two op-amp golden rules and know when they apply (negative feedback present)
- 02Use an op-amp open-loop as a comparator whose output clamps to a supply rail
- 03Derive and apply the inverting gain Vout = -(R2/R1)Vin from the virtual-ground idea
- 04Derive and apply the non-inverting gain Vout = (1 + R2/R1)Vin, and the unity-gain buffer
- 05Apply the difference amplifier Vout = (R2/R1)(V2 - V1) and see common-mode rejection
- 06Find the saturation point Vin,sat = Vrail/|A| and check outputs against the rails
- 07Explain high input impedance, low output impedance, and the ~20-40 mA current limit
- 08Avoid the classic sign, ratio-direction and saturation mistakes under exam precision rules
Non-inverting amplifier: gain, output and saturation
- +1Golden rules: the signal is on the non-inverting input, so V+ = Vin = 0.6 V, and by Rule 1 the inverting input follows: V- = V+ = 0.6 V.
- +1Non-inverting gain: A = 1 + R2/R1 = 1 + 18 kilo-ohm / 2 kilo-ohm = 1 + 9 = 10 (dimensionless).
- +1Output: Vout = A x Vin = 10 x 0.6 V = 6.0 V, which lies within plus/minus 15 V, so the stage is linear (not saturated).
- +1Saturation input: the output first hits a rail when |A x Vin| = Vrail, so Vin,sat = Vrail / A = 15 V / 10 = 1.5 V.
- +1Interpret: any input above 1.5 V (or below -1.5 V) pins the output to the plus/minus 15 V rail; at 0.6 V we sit comfortably in the linear region.
Key terms
- Operational amplifier (op-amp)
- A very-high-gain differential amplifier with two inputs (inverting V- and non-inverting V+) and one output. Used open-loop as a comparator, or with negative feedback as a precise amplifier.
- Golden rules
- The two ideal assumptions used with negative feedback: (1) the inputs are driven to the same voltage, V+ = V-; (2) the input terminals draw essentially no current, i is approximately 0 A.
- Comparator
- An op-amp used open-loop (no feedback). If V+ > V- the output clamps to the high rail; if V+ < V- it clamps to the low rail. It turns an analog level into a one-bit decision at a threshold.
- Inverting amplifier
- Signal in through R1 to V-, feedback R2, V+ grounded. Gain Vout = -(R2/R1)Vin: output is inverted (opposite sign), and its input impedance equals R1.
- Non-inverting amplifier
- Signal to V+ directly, R1 from V- to ground, feedback R2. Gain Vout = (1 + R2/R1)Vin: same polarity, always at least 1, and a very high input impedance.
- Difference amplifier
- Matched resistor pairs amplify the gap between two inputs: Vout = (R2/R1)(V2 - V1). Any voltage common to both inputs cancels, which is why it reads small differential sensor signals.
- Saturation
- An op-amp output cannot exceed its supply rails. For gain A the linear range ends at Vin,sat = Vrail/|A|; beyond it the output simply sits at the rail and the gain formula no longer applies.
- Virtual ground
- In the inverting amplifier the golden rules hold the inverting node at 0 V even though no wire connects it to ground, because V+ is grounded and feedback forces V- = V+.
Op-Amps: Comparators & Amplifiers FAQ
Can AI help me with op-amp circuits in AMME1705?
Yes, as a study aid. Sia, the AI tutor in the AskSia library, explains op-amp problems step by step: it can walk you through why the inverting gain carries a minus sign, how the golden rules give a virtual ground, or how to check an output against the supply rails, using your own practice numbers. It is built to help you understand and practise the method, not to hand you answers to an assessed exam or quiz, and it never guarantees a grade — use it to learn the reasoning so you can reproduce it under exam conditions.
How do I tell an inverting from a non-inverting amplifier?
Look at where the signal enters. If the input goes through a resistor to the inverting input (V-) while V+ is grounded, it is inverting, gain -(R2/R1). If the signal drives the non-inverting input (V+) directly, it is non-inverting, gain 1 + R2/R1. The non-inverting form always has the leading '1' and never flips sign; the inverting form never has the '1' and always flips sign.
Do I have to memorise the op-amp formulas for the exam?
The final is a restricted-materials paper: you may bring a calculator and, per the exam cover sheet, one A4 double-sided handwritten note sheet, though the assessment table lists the paper as closed book — confirm the current status on your Canvas assessment page. Either way, the device parameters (gain, rail voltages, resistor values) are given in each question, but you are expected to supply the gain and saturation relationships yourself, so keep the four core forms on your note sheet and in your head.
Studying with AI? Sia — free AI electrical engineering tutor works through AMME1705 step by step.
Exam move
Anchor everything to the two golden rules: once you can say 'V+ = V- and the inputs draw no current', every configuration falls out by writing one node equation. Practise deriving the inverting and non-inverting gains from scratch a few times rather than memorising them cold, because a derivation you own survives a stressful exam better than a formula you half-remember. Drill the sign discipline (inverting is negative), the ratio direction (feedback over input, R2/R1), and the always-check-the-rails habit, since these are where marks quietly leak. The written final runs for two hours of writing plus ten minutes of reading and is worth 33 percent of the unit; the practice paper totals 80 marks, so budget roughly one and a half minutes per mark and confirm the mark total on your paper's cover. Answers must match the stated precision, so carry full precision through your working and round only on the last line.
