Linear integrated circuits (linear ICs) are analog chips that process continuously varying signals: op-amps, timers, voltage regulators, comparators, phase-locked loops and data converters. This page works the calculations linear IC courses test, from 555 timer frequency and LM317 resistor choice to Schmitt trigger thresholds, PLL lock range and DAC resolution, each with real component values. FLN Tutors (Freelancer Network) also offers one-to-one help. Matched to a verified specialist who knows your course, your university's marking criteria, and your deadline.
Topics we cover
FLN offers one-to-one online Linear integrated Circuits tutoring with verified subject specialists. Sessions focus on calculations, design problems and the theory behind them, including Operational Amplifiers, Comparators, Active Filters and Oscillators, using your own course material, so you understand the subject and can apply it yourself.
Last updated
An integrated circuit puts transistors, resistors and sometimes capacitors on one piece of silicon. A linear (analog) IC works with signals that vary continuously, where a digital IC works with two levels, 0 and 1.
| Family | Common ICs | What they do |
|---|---|---|
| Operational amplifiers | 741, LM358, TL081 | Amplify, add, integrate, filter |
| Timers | 555, 556 | Generate pulses and square waves |
| Voltage regulators | 7805, 7812, LM317 | Hold a supply voltage steady |
| Comparators | LM311, LM339 | Compare two voltages and switch |
| Phase-locked loops | 565, CD4046 | Lock onto and track a frequency |
| Data converters | DAC0808, ADC0804 | Convert between analog and digital |
Classification examiners ask for: by function, linear versus digital; by scale of integration, SSI, MSI, LSI and VLSI; and by package, the 8-pin DIP used by the 741 and 555 being the one to draw.
For ideal op-amp configurations, real op-amp limitations and filter cutoff calculations, see the analog electronics page; this page concentrates on the specific ICs and their design calculations.
The 741 is the op-amp most syllabuses use to teach specifications, even though modern designs usually choose a better part.
| Pin | Function |
|---|---|
| 1 and 5 | Offset null |
| 2 | Inverting input (−) |
| 3 | Non-inverting input (+) |
| 4 | Negative supply, −V |
| 6 | Output |
| 7 | Positive supply, +V |
| 8 | No connection |
| Parameter | Typical value for the 741 | Ideal op-amp |
|---|---|---|
| Open-loop voltage gain | 200,000 (106 dB) | Infinite |
| Input resistance | 2 MΩ | Infinite |
| Output resistance | 75 Ω | Zero |
| Input offset voltage | 1 mV | Zero |
| Input bias current | 80 nA | Zero |
| CMRR | 90 dB | Infinite |
| Slew rate | 0.5 V/µs | Infinite |
| Gain-bandwidth product | about 1 MHz | Infinite |
How to use the table in an answer: state the typical value, then the ideal value, then what the difference does in practice. The low slew rate, for example, is why a 741 cannot reproduce a large, fast square wave.
In astable mode the 555 runs continuously, producing a square wave. The capacitor charges through RA and RB and discharges through RB only:
With RA = 4.7 kΩ, RB = 10 kΩ and C = 10 nF:
| Quantity | Working | Result |
|---|---|---|
| t_high | 0.693 × 14.7 kΩ × 10 nF | 101.87 µs |
| t_low | 0.693 × 10 kΩ × 10 nF | 69.3 µs |
| Period T | 101.87 + 69.3 | 171.17 µs |
| Frequency | 1 ÷ 171.17 µs | 5,842 Hz |
| Duty cycle | 101.87 ÷ 171.17 | 59.5% |
The 1.44 shortcut gives 5,830 Hz. The small difference comes from rounding 1 ÷ 0.693 to 1.44, so say which formula you used.
Why the duty cycle is always above 50%: the capacitor charges through both resistors but discharges through RB alone, so t_high is always longer. A diode across RB lets it charge through RA only, which allows a duty cycle of 50% or less.
Monostable mode gives one pulse per trigger, of width T = 1.1 RC. With R = 100 kΩ and C = 10 µF, T = 1.1 × 100,000 × 0.00001 = 1.1 seconds.
Fixed regulators. The 78xx series gives a fixed positive output: 7805 gives 5 V and 7812 gives 12 V, while the 79xx series gives negative outputs. Each needs its input about 2 V above the output, called the dropout voltage, so a 7805 needs at least about 7 V in.
The heat they produce is the calculation students forget. A regulator burns off the difference between input and output:
P = (V_in − V_out) × I
A 7805 fed from 12 V and supplying 0.5 A dissipates (12 − 5) × 0.5 = 3.5 W, which needs a heatsink.
Adjustable regulator: worked LM317 design. The LM317 holds 1.25 V between its output and adjust pins, so:
V_out = 1.25 × (1 + R2 ÷ R1), ignoring the small adjust-pin current
For 12 V, R2 = 2.2 kΩ gives 1.25 × (1 + 2,200 ÷ 240) = 12.708 V.
A comparator switches when its input crosses a reference. With a noisy input, it can switch many times around that point. A Schmitt trigger adds positive feedback, giving two thresholds so that the output switches cleanly once.
Inverting Schmitt trigger: the input goes to the inverting pin, and R1 (feedback) and R2 (to ground) feed a fraction of the output back to the non-inverting pin. The feedback fraction is β = R2 ÷ (R1 + R2).
With output saturation at ±13 V, R1 = 10 kΩ and R2 = 2.2 kΩ:
The output only changes state when the input rises above +2.34 V or falls below −2.34 V, so noise smaller than 4.69 V peak to peak cannot cause false switching.
The trade-off to mention: more hysteresis rejects more noise, but the input must swing further before the output responds. Choose R2 to suit the noise you expect.
An instrumentation amplifier amplifies the small difference between two inputs while rejecting voltages common to both. That makes it the standard choice for strain gauges, thermocouples and ECG electrodes.
The three-op-amp design. Two input buffers share a gain resistor R_G, followed by a difference amplifier. With equal resistors R in the first stage and a unity-gain difference stage:
G = 1 + 2R ÷ R_G
With R = 10 kΩ and R_G = 1 kΩ: G = 1 + 20,000 ÷ 1,000 = 21.
Changing one resistor, R_G, sets the gain without upsetting the balance of the circuit. That single-resistor adjustment is the reason the design exists.
Single-chip versions give the gain formula on the datasheet. A common part uses G = 1 + 49.4 kΩ ÷ R_G, so a gain of 100 needs R_G = 49.4 kΩ ÷ 99 = 499 Ω, which is a standard 1% value.
Why not use one op-amp? A single difference amplifier has low input resistance and needs four matched resistors to keep a high CMRR. The instrumentation amplifier has very high input resistance on both inputs and keeps its CMRR when the gain is changed.
A phase-locked loop compares the phase of an input signal with a voltage-controlled oscillator (VCO) and adjusts the VCO until the two match. Its three blocks are the phase detector, a low-pass filter and the VCO. PLLs are used for FM demodulation, frequency synthesis and clock recovery.
Two ranges to define:
Worked with the standard textbook relations for the 565, with R1 = 10 kΩ, C1 = 0.01 µF, supplies of ±10 V (so V = 20 V) and filter capacitor C2 = 10 µF:
| Quantity | Formula | Result |
|---|---|---|
| Free-running frequency | f0 = 0.3 ÷ (R1 C1) | 3,000 Hz |
| Lock range | f_L = ±8 f0 ÷ V | ±1,200 Hz |
| Capture range | f_C = ±(1 ÷ 2π) √(2π f_L ÷ (3.6 × 10³ × C2)) | ±72.84 Hz |
The capture range is always narrower than the lock range, which is the comparison examiners ask for. Increasing C2 narrows the capture range further, rejecting more noise but making lock slower to acquire.
A digital-to-analog converter (DAC) turns a binary number into a voltage. The R-2R ladder is the usual design taught, because it needs only two resistor values however many bits there are.
Resolution of an 8-bit DAC with a 5 V reference:
An analog-to-digital converter (ADC) does the reverse. The successive-approximation type tests one bit per clock cycle, so an 8-bit conversion with a 1 MHz clock takes about 8 × 1 µs = 8 µs, plus a few cycles of overhead. Flash ADCs are much faster but need 2ⁿ − 1 comparators, which is why they are limited to low resolutions.
The step size is the smallest voltage change the system can represent. Quantisation error is up to half of one step either way.
See analog electronics help for op-amp configurations, real op-amp limits and filters, digital electronics help for logic and counters, power electronics help for switching converters, microcontrollers help for timers and ADCs on a chip, and electrical measurements help for measuring the circuits you build.
If a 555, regulator or PLL calculation will not come out right, send it over with your working and a tutor will show you where it goes wrong.
Stuck on a Linear integrated Circuits question?
Send it to a Linear integrated Circuits tutor for step-by-step working. The quote is free.
What you get
Simple process
Tell us your assignment brief, word count, deadline, and academic level. The more detail, the better the match.
We pair you with a Linear integrated Circuits expert whose background aligns with your specific topic and university requirements.
Your work arrives before the deadline, plagiarism-checked. Free revisions until it meets your exact requirements.
Takes about two minutes. The quote is free.
Linear integrated Circuits and related specialists
Every expert is degree-verified and quality-tested before joining.
I am a BITS Pilani graduate in Electronics and Electrical Engineering, with minors in Mathematics and Physics and a strong focus on Artificial Intelligence, Machine Learning, and Agentic AI. I have 7 years of experience providing tutoring, academic project guidance, and thesis…
I am an Analog and RF IC Design Engineer and Project Lead specializing in high-speed, high-performance circuit design across advanced FinFET technologies. My experience spans TSMC 2nm, 3nm, 7nm, 16nm, 28nm, 65nm, and Samsung 8nm, with expertise in high-speed SerDes, line…
I am a Ph.D. in Electronics & Communication Engineering with 10+ years of teaching experience and am currently working as an Assistant Professor in the Electronics and Communication Engineering Department at Academy of Technology. Previously, I served as a Postdoctoral Research…
I am an Advanced Electronics and Embedded Systems expert specializing in Digital Electronics, Microcontrollers, FPGA & Verilog, Circuit Design, and Computer Architecture. Skilled in C/C++ programming, IoT, Computer Networks, and hardware–software integration, with a focus on…
Student reviews
Used FLN Tutors? Be one of the first to share how it went, in writing or in a short video.
A linear integrated circuit is an analog chip that processes signals varying continuously, rather than switching between two digital levels. Common examples are operational amplifiers such as the 741, the 555 timer, voltage regulators such as the 7805 and LM317, comparators, phase-locked loops and data converters.
Linear ICs handle signals that can take any value within a range, such as audio or sensor outputs, and their output is proportional to their input. Digital ICs handle only two levels, representing 0 and 1, and perform logic, counting and storage. Many systems use both together.
Pin 2 is the inverting input, pin 3 the non-inverting input, pin 4 the negative supply, pin 6 the output and pin 7 the positive supply. Pins 1 and 5 are used for offset null adjustment, and pin 8 has no connection in the standard 8-pin package.
Typical values are an open-loop gain of about 200,000, input resistance of 2 megohms, output resistance of 75 ohms, input offset voltage of 1 millivolt, CMRR of 90 decibels and slew rate of 0.5 volts per microsecond. An ideal op-amp would have infinite or zero values instead.
Calculate the high time as 0.693 times RA plus RB times C, and the low time as 0.693 times RB times C. Add them for the period and take the reciprocal. With RA of 4.7 kilohms, RB of 10 kilohms and 10 nanofarads, the frequency is about 5,842 hertz.
The timing capacitor charges through both RA and RB but discharges through RB alone, so the high time is always longer than the low time. Adding a diode across RB makes the capacitor charge through RA only, which allows a duty cycle of 50 per cent or lower.
The output pulse width of a 555 monostable is 1.1 times the timing resistance times the timing capacitance. A 100 kilohm resistor with a 10 microfarad capacitor gives a pulse of 1.1 seconds each time the circuit is triggered. The pulse length does not depend on the supply voltage.
The output equals 1.25 volts multiplied by one plus R2 divided by R1, ignoring the small adjust-pin current. With R1 of 240 ohms, a 5 volt output needs R2 of 720 ohms; the nearest standard value of 750 ohms gives about 5.16 volts.
Dropout voltage is the minimum difference between input and output at which a regulator can still hold its output steady. For the 78xx series it is about two volts, so a 7805 needs roughly seven volts or more at its input to deliver a stable five volts.
A linear regulator dissipates the input voltage minus the output voltage, multiplied by the load current. A 7805 running from 12 volts and supplying half an amp dissipates 3.5 watts, which needs a heatsink. Higher input voltages waste more power, which is why switching regulators are often preferred.
A Schmitt trigger is a comparator with positive feedback that gives two switching thresholds instead of one. The output changes state only when the input rises above the upper threshold or falls below the lower one, so noise smaller than the hysteresis gap cannot cause false switching.
Find the feedback fraction, R2 divided by R1 plus R2, and multiply it by the positive and negative saturation voltages. With saturation at 13 volts, R1 of 10 kilohms and R2 of 2.2 kilohms, the thresholds are about plus and minus 2.34 volts, giving 4.69 volts of hysteresis.
An instrumentation amplifier amplifies the small difference between two signals while rejecting voltages common to both inputs. It has very high input resistance and a high common-mode rejection ratio, making it the standard choice for strain gauges, thermocouples, bridge circuits and medical electrodes such as ECG sensors.
Lock range is the band of input frequencies over which a phase-locked loop stays locked once it has locked. Capture range is the narrower band over which it can acquire lock from an unlocked state. The capture range is always smaller, and it narrows further as the loop filter capacitance increases.
Yes. A one-to-one tutor can work through 555 timer, regulator, Schmitt trigger, instrumentation amplifier, PLL and data converter calculations with you, and check where your working goes wrong. You complete your own assessed work and lab reports in line with your college or university's academic rules.
Question not answered here?
Related areas
Not sure which service you need?
Tell us your assignment brief and deadline — we'll match you with the right expert and service instantly.
Full refund if we miss the agreed deadline, can't find a suitable expert, or major errors can't be fixed by revision.
Learn more →Your identity, order details and institution are never shared with any third party.
Learn more →Every order has an agreed deadline. If we don't deliver by it, you can claim a full refund.
Learn more →Get started today
Tell us what you need and get matched with a tutor who teaches your subject. Delivered on time, every time.
