• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar

Homemade Circuit Projects

Get free circuit help 24/7

  • 1000+ Circuits
  • Privacy Policy
  • About Us
  • Contact
  • Disclaimer
  • Videos – Circuit Test Results
You are here: Home / Inverter Circuits / How to Calculate Modified Sine Waveform

How to Calculate Modified Sine Waveform

Last Updated on May 21, 2019 by Swagatam 4 Comments

I am sure you might have often wondered how to accomplish the correct way of optimizing and calculating a modified square wave such that it produced almost an identical replication of a sine wave when used in an inverter application.

The calculations discussed in this article will help you to learn the technique through which a modified square wave circuit could be turned into sinewave equivalent. Let's learn the procedures.

The first criterion to accomplish this is to match the RMS value of the modified square with the sinewave counterpart in a way that the result replicates the sinusoidal waveform as closely as possible.

What is RMS (Root Mean Square)

We know that the RMS of our home AC sinusoidal waveform voltage is determined by solving the following relationship:

Vpeak = √2 Vrms

Where Vpeak is the maximum limit or the peak limit of the sine waveform cycle, while the mean magnitude of the each cycle of the waveform is shown as the Vrms

The √2 in the formula helps us to find the mean value or the net value of an AC cycle which changes its voltage exponentially with time. Because the sinusoidal voltage value varies with time and is a function of time, it cannot be calculated by employing the basic average formula, instead we depend on the above formula.

Alternatively, AC RMS could be understood as an equivalent to that value of a direct current (DC) which produces an identical average power dissipation when connected across a resistive load.

OK, so now we know the formula for calculating the RMS of a sinewave cycle with reference to its peak voltage value.

This can be applied for evaluating the peak and the RMS for our home 50 Hz AC too. By solving this we get the RMS as 220V and peak as 310V for all 220V based mains AC systems.

Calculating Modified Square Wave RMS and Peak

Now let's see how this relationship could be applied in modified square wave inverters for setting up the right waveform cycles for a 220V system, which would correspond to a 220V AC sinusoidal equivalent.

We already know that the AC RMS is equivalent to the average power of a DC waveform. Which gives us this simple expression:

Vpeak = Vrms

But we also want the peak of the square wave to be at 310V, so it seems the above equation won't hold good and cannot be used for the purpose.

The criteria is to have 310V peak as well as an RMS or average value of 220V for each square wave cycle.

To solve this correctly we take the help of the ON/OFF time of the square waves, or the duty cycle percentage as explained below:

Each half cycle of a 50 Hz AC waveform has a time duration of 10 millisecond (ms).

A modified half wave cycle in its most crude form must look like as shown in the following image:

how to calculate modified square wave RMS and peak

We can see that the each cycle begins with a zero or blank gap, then shoots up to 310V peak pulse and again ends with a 0V gap, the process then repeats for other half cycle.

In order to achieve the required 220V RMS we have to calculate and optimize the peak and the zero gap sections or the ON/OFF periods of the cycle such that the average value produces the required 220V.

The grey line represents the 50% period of the cycle, which is 10 ms.

Now we need to find out the proportions of the ON/OFF time which will produce an average of 220V. We do it in this way:

220 / 310 x 100 = 71 % approximately

This shows that the 310V peak in the above modified cycle should occupy 71% of the 10 ms period, while the two zero gaps should be 29% combined, or 14.5% each.

Therefore in a 10 ms length, the first zero section should be 1.4 ms, followed by the 310 V peak for 7 ms, and finally the last zero gap of another 1.4 ms.

Once this is accomplished we can expect the output from the inverter to produce a reasonably good replication of a sine waveform.

modified AC calculations

Despite of all these you may find that the output is not quite an ideal replication of the sine wave, because the discussed modified square wave is in its most basic form or a crude type. If we want the output to match the sine wave with maximum precision, then we have to go for an SPWM approach.

I hope the above discussion might have enlightened you regarding how to calculate and optimize a modified square for replicating sinewave output.

For practical verification, the readers can try applying the above technique to this simple modified inverter circuit.

Here's another classic example of an optimized modified waveform for getting a good sine wave at the secondary of the transformer.




Previous: What is beta (β) in BJTs
Next: Loud Pistol Sound Simulator Circuit

About Swagatam

I am an electronic engineer (dipIETE ), hobbyist, inventor, schematic/PCB designer, manufacturer. I am also the founder of the website: https://www.homemade-circuits.com/, where I love sharing my innovative circuit ideas and tutorials.
If you have any circuit related query, you may interact through comments, I'll be most happy to help!

You'll also like:

  • 1.  Optimizing Grid, Solar Electricity with Inverter
  • 2.  How to Build a 220V DC Inverter UPS Circuit
  • 3.  Automatic Inverter Fan Switch ON while Charging and Inverting Modes
  • 4.  300 Watts PWM Controlled Pure Sine Wave Inverter Circuit
  • 5.  7 Simple Inverter Circuits you can Build at Home
  • 6.  500 Watt Inverter Circuit with Battery Charger

Please Subscribe (Only if you are Genuinely Interested in our Newsletters)


 

Reader Interactions

Comments

    Your Comments are too Valuable! But please see that they are related to the above article, and are not off-topic! Cancel reply

    Your email address will not be published. Required fields are marked *

  1. Search Related Posts for Commenting

  2. cleber de oliveira gonçalves says

    gostei muito dos projetos exelentes

    Reply
    • Swagatam says

      Que bom que você gostou deles

      Reply
  3. holawaleh says

    great work and explanation. thumb up!.
    I want to ask how can I incorporate this into an inverter circuit. I mean to get desired results from MOSFET

    Reply
    • Swag says

      Thank you holawaleh,

      you can implement this quite effectively using an IC 555 and IC 4017 based inverter circuit. Since IC 4017 has 10 outputs, we can optimize 5 outputs for one channel and other 5 for the other channel in a center tap based inverter circuit

      From these 5 outputs skip the 1st and the 5th (keep them unconnected), and combine the middle 3 pins through diodes and join the diode ends with the gate of the mosfet. Do this for both the channels. This will quite effectively allow you to accomplish a 310V peak and a 220V RMS sine wave at the transformer output.

      Reply


  4. COMMENT BOX IS MOVED AT THE TOP


Primary Sidebar

Electronic Projects Categories

  • 3-Phase Power (15)
  • 324 IC Circuits (19)
  • 4017 IC Circuits (51)
  • 4060 IC Circuits (25)
  • 555 IC Circuits (92)
  • 741 IC Circuits (18)
  • Amplifiers (49)
  • Arduino Engineering Projects (82)
  • Audio Projects (84)
  • Battery Chargers (75)
  • Car and Motorcycle (87)
  • Datasheets (45)
  • Decorative Lighting (Diwali, Christmas) (31)
  • DIY LED Projects (81)
  • Electronic Components (97)
  • Electronic Devices and Circuit Theory (35)
  • Electronics Tutorial (99)
  • Fish Aquarium (5)
  • Free Energy (34)
  • Games (2)
  • GSM Projects (9)
  • Health Related (17)
  • Heater Controllers (23)
  • Home Electrical Circuits (98)
  • Incubator Related (6)
  • Industrial Electronics (26)
  • Infrared (IR) (39)
  • Inverter Circuits (94)
  • Laser Projects (10)
  • LM317/LM338 (21)
  • LM3915 IC (24)
  • Meters and Testers (54)
  • Mini Projects (153)
  • Motor Controller (64)
  • MPPT (7)
  • Oscillator Circuits (12)
  • PIR (Passive Infrared) (8)
  • Power Electronics (33)
  • Power Supply Circuits (66)
  • Radio Circuits (9)
  • Remote Control (46)
  • Security and Alarm (56)
  • Sensors and Detectors (115)
  • SG3525 IC (5)
  • Simple Circuits (72)
  • SMPS (30)
  • Solar Controllers (60)
  • Timer and Delay Relay (51)
  • TL494 IC (5)
  • Transformerless Power Supply (8)
  • Transmitter Circuits (38)
  • Ultrasonic Projects (12)
  • Water Level Controller (45)

Follow Homemade Circuits

Facebook
Twitter
YouTube
Instagram
My Facebook-Page
Quora

Feeds

Post RSS
Comment RSS

Circuit Calculators

  • AWG to Millimeter Converter
  • Battery Back up Time Calculator
  • Capacitance Reactance Calculator
  • IC 555 Astable Calculator
  • IC 555 Monostable Calculator
  • Inductance Calculator
  • LC Resonance Calculator
  • LM317, LM338, LM396 Calculator
  • Ohm’s Law Calculator
  • Phase Angle Phase Shift Calculator
  • Power Factor (PF) Calculator
  • Reactance Calculator
  • Small Signal Transistor(BJT) and Diode Quick Datasheet
  • Transistor Astable Calculator
  • Transistor base Resistor Calculator
  • Voltage Divider Calculator
  • Wire Current Calculator
  • Zener Diode Calculator

© 2021 · Swagatam Innovations