# Why sine wave not square wave?

Rectifying square wave voltage seems to give us DC directly without the need of a capacitor. so, why do we prefer sine wave over it?
What would change if I powered any adapter (laptop adapter as example) or any power supply with a square wave inverter instead of sine wave?

Edit: I understood from answers and comments that sine wave is better at generating and transmission, let's consider this a special case about "Powering power supplys (with input rectification) with inverters."

• Or why even using AC? Using DC would give us DC even without the need for rectifying (I am asking this silly question to give some hints to find the answer yourself)
– Curd
Sep 3, 2016 at 17:04
• Good question. If we accept the premise that a square wave would be more convenient at the point of use, then the answer must have something to do with the difficulties that would cause for power generation and transmission. What do you suppose those could be? Sep 3, 2016 at 17:08
• try sending a square wave and all those harmonics down a few km of overhead lines... Rectification isn't the only thing to consider, how would you transform one squarewave potential to another
– user16222
Sep 3, 2016 at 17:21
• @JonRB I think it's different, smps uses very high frequencies not 50hz and it's transformer has small leakage inductance. If you used square wave with 50hz transformer, the output would be spikes as the transformer will respond only to the eqges of the square wave. Sep 3, 2016 at 17:53
• Square waves would be much more difficult to generate. Square waves might be much more difficult to switch (not sure if the arc will extinguish during the very fast crossover). Square waves will generate more electrical noise. Square waves will be very difficult to keep square over long range and through transformers. I think square waves create a lot more problems than they solve. Sep 3, 2016 at 17:54

There are a number of crucial elements to consider when choosing an infrastructure

1. How to generate
2. How to transmit
3. How to utilise
4. How economical

GENERATION

Generation is via electrical machines and almost all will generate Alternating current with a SINUS profile & the simplest is a wound-rotor sync machine & thus we have a source that is sinus [a]

TRANSMISSION

Let's assume we have generated a square-wave voltage source of a frequency suitable for SMPS... 50kHz-100kHz. We now need to move the power from generation to consumption USING the Tesla model.

During the Current wars Edison advocated DC & community generation. Tesla advocated AC & centralised generation.

With centralised generation the power stations are 10's of km away from consumption. To minimise losses this "squarewave" would need to be high-voltage (400kV) while also holding the characteristics of a squarewave (ie harmonics...).This would entail a dv/dt in excess of 400kV per us (assuming a pessimistic acceptable risetime...), likewise the inductance of the transmission line is quite significant. This will result in at least three things

1. The end waveform will NOT be square in shape
2. There will be extremely high voltage overshoots at the load end due to the transmission line.
3. The EMI around those overheads would be extremely disruptive. Could they be all buried instead? sure but the infrastructure cost would be astronomical.

Lets forget about this for a moment and accept that we have received a reasonable squarewave at 400kV with about 100kVA behind it... this needs to be transformed to a level that can be consumed. You are wanting to consider PSU's... You would not want to feed 400kV into a supply (Safety and other annoyances...) so this would need to be stepped down...

Could that be made? sure I guess but the power electronics involved isn't trivial BUT does exist. Take all the HVDC systems in existence. This square-wave would then need to be rectified to then be stepped down. Why bother with those extra diodes and just transmit in HVDC instead? Current wars... (see economics)

Even if an Edison generation model was considered the three named issues would still exist.

This only considers the bulks transmission of power. There is then the residential aspect as this 400kV is stepped down to 125kv down to 12kV .. 240V.

UTILISATION

In "modern society" we appear to use a lot of low-voltage DC fed equipment (chargers, PC, TV...) but they are not the high-power demanding devices (washers, heaters, vacuum...) and this is before considering industry.

One thing that is FANTASTIC about the UK is its unquenchable thirst for statistics, 2nd to none.

## In 2015

Home 9300 ktoe (ktoe = Thousands of tonnes of oil equiv)

Industry: 7940 ktoe

Commercial: 6402 ktoe

Some domestic is only 39% of electrical consumption

Concentrating PURELY on electrical power consumption, this is further split:

1. Computers: 164 ktoe
2. Monitors: 100 ktoe
3. Printers: 299 ktoe
4. Refrigeration: 2602 ktoe
5. Aircon: 1812 ktoe
6. Motors: 11564 ktoe
7. Circulators: 275 ktoe
8. Displays: 702 ktoe
9. Lighting: 397 ktoe
10. Office: 4126 ktoe
11. Street lighting: 264 ktoe

Those three highlighted account for 71% of all electrical consumption in the UK (motors alone are 51%)

The bulk require AC to function so with the blinkered view of SMPS driving a legitimate question "why not a squarewave" ignores what utilises it the most

ECONOMICS

To implement an electrical network takes a lot of time, money and resource & this was all initiated around the turn of the last century.

Edison: DC & Local generation

Tesla: AC & Centralised generation.

Tesla won in the end with AC mainly due to the economics of transformation. In the following decades many countries then started building their infrastructure around a wide variety of frequencies but eventually settling on 50Hz or 60Hz.

At the time what was capable of consuming electricity? Lighting (either AC or DC...) Heating (either AC or DC) Motors (low power at the time.. only AC or DC, not mixed.)

Why these frequencies? This is lost in time... but manufacturing capabilities would have had a large say in the matter... The laminations of a generators corepack could only reliably be made so thin, the same with XFMR laminations. Bearing only capable of withstanding a certain velocity...

And so we now have an electrical infrastructure built at a time of war, limited resource and technical ability. There was no power electronics todo any clever DC:DC conversion...

Today? if we were to rip up the entire system would we stick with 50Hz AC? probably... it is very convenient for transmission. HVDC is very economical over long distances and high powers.

Why would we want to transmit a high power square wave (if we could...) when high-voltage DC would be soo much simpler and HVAC is soo easy to manage.

In a domestic environment there could be an argument to have a LVDC ring as well as a LVAC ring due to all the additional DC-fed appliances and the "efficiencies of SMPS" but you have to be careful with a DC-bus ... they go unstable. Maybe there is a future in a 48V LVDC ring in each house but this LVDC ring is locally created rather than supplied by the local substation.

[a] Not all machines generate AC.. BrushedDC produces DC but you would not consider such machine topology anywhere near grid power-levels. SR machine+inverter will generate onto a DCbus but you will need an inverter to do this (additional cost, complexity etc...)

Because square waves are not physical.

Even for your revised question about "[p]owering power supplys [sic] (with input rectification) with inverters," you cannot get away with using some form of energy storage (e.g. capacitors) during the time where the input transitions between positive voltage and negative voltage. The full voltage after your putative magical rectifier cannot be maintained at those times. What you observe instead are periodic dips at the output rather than the nice flat line in your question.

Furthermore, a typical bridge rectifier has a dead zone passing through the low-voltage zone on account of the 0.7V or so turn-on voltage threshold in semiconductor devices. That just makes the problem worse.

• I don't think you're properly explaining why capacitors are still required. If anything, the square wave may reduce the total bulk capacitance required to maintain a low ripple out of the rectifier. Sep 3, 2016 at 23:55

Yes, but note the difference in peak vs RMS voltages: The rectifier in the power supply tends to go towards the PEAK voltage of the input waveform, so for 120V line input, the DC output is somewhere like 160-170VDC. If you were to use a 120V RMS square wave, the DC output would approach 120VDC.

• but how would you generate it?
– user16222
Sep 3, 2016 at 17:13
• ... with an alternator with a triangle-form rather than a sine-form magnetic field. Sep 3, 2016 at 18:16
• @Neil_UK was more a rhetorical question
– user16222
Sep 3, 2016 at 18:19

Don't listen to these guys; you and I, with the passion to make homes run off of square wave power, can and will develop domestic electrical supplies and appliances to produce and use ac square wave (ACSW© (pending copyright)) a soon-to-be staple of homes across the world!

In all seriousness, if square wave power were practical for in-home use, I would not have to battle against the 60 cycle hum with every piece of audio equipment I've ever owned- for that reason alone I think square wave AC has at least some potential application in spite of the responses of the other finely educated and rather cynical users.

• Do you want to battle against 180 Hz, 300 Hz, 420 Hz, 540 Hz, ....( and a lot more) ? Jul 13, 2018 at 5:30
• Look at mathematical representation of square wave. Jul 13, 2018 at 5:32