Does it exist an AC to AC converter in small package for converting 220v to 110v?

[kripacharya]

Conduction angle is in fact about 65 degrees i.e. the first, or last 65 degrees of each half cycle, if you want 110V rms from 230Vrms

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View attachment 154387 per the above ...

Very useful graph!
Firing angle is seen to be ~65° in first and last part of cycle to achieve 110Vrms from a 220Vrms signal.

At 65°, peak voltage would then be:
220 x √2 x sin(65) = 282 volts. Not that much different from 220x1.414 and still exceeding peak of 110Vrms signal by more than 125 volts.

 

[c_mitra]

if you want 110V rms from 230Vrms...

I do not understand the graph you have attached: why the RMS and the power graphs are different? They should be identical.

There are some hidden assumptions here.

 

[kripacharya]

I do not understand the graph you have attached: why the RMS and the power graphs are different? They should be identical.

There are some hidden assumptions here.

Yes. The "hidden assumption" is that power is proportional to square of voltage, and also "hidden" is that graph is normalised.

 

[Easy peasy]

Very useful graph!
Firing angle is seen to be ~65° in first and last part of cycle to achieve 110Vrms from a 220Vrms signal.

the word AND in the above quote makes the sentence incorrect, you can have the first 65 degC or the last in an half cycle - but not both - for 110Vac rms from 230Vrms ...

unless that is what the poster was trying to say ...

 

[kripacharya]

the word AND in the above quote makes the sentence incorrect, you can have the first 65 degC or the last in an half cycle - but not both - for 110Vac rms from 230Vrms ...

unless that is what the poster was trying to say ...

You are right! I was referring to (full) cycle of 360° while the initial posting referred to each half-cycle of 180°. Thanks for clarification