Design a circuit having 120vac:22mA input to drive a LED requiring
3v-max 3.5 and 25mA.Assume wiring has zero resistance. Thank you very
much.billkirk

The specified input power is 2.64 watts, so the transformer needs to
be reasonably efficient, even though the output is only 0.875 watts
max. DC power cubes are likely available that meet all these specs
except the no load voltage likely will exceed 3.5 volts.(Current
rating of more than 25 milliamps is ok, except you may exceed the 22
milliamps input current)
Over 3.5 volts can be corrected with a one watt zener diode rated 2.7
volts + or minus 20% or 3 volts plus or minus 10%. Alternately you can
connect 5 common silicon diodes in series to serve as the zener diode.
If the voltage is below 2.9 volts, you will need a 6th silicon diode.
If you get 3 volts and want a bit more, you can use a germainium diode
or other type with about 0.2 volts forward drop. An extra diode can
also be added to the zener to get either 0.2 or 0.6 volts more or one
of each for 0.8 volts more.
If you decide to buy a transformer or use an AC power cube, the output
voltage needs to be between 2.5 volts and 3.5 volts at 25 ma or more.
If it is rated lots more than 25 ma, you will likely run over the 22
ma input current spec. I presume 22 ma is not an exact requirement. ie
19 ma is ok.
All the readings will decrease a few percent if you connect a 1/40 to
a 1/10 th amp fuse in series with the ac power.
Try a single silicon diode as the rectifier. LED prefer pulses to well
filtered dc, but measurments are tricky. Most volt meters will read
more than 3 volts applied to the LED (you need a true RMS dc
voltmeter) Most meters will read more than 25 milliamps (you need a
true RMS dc milliampmeter) or you can just guess that 3.7 volts at 29
ma is ok for the LED. Many meters are rather inaccurate even for well
filtered dc.
If the voltage to the LED is low, you can add a 10 micro farad
capacitor from the rectifier to ground. More capacity will increase
the voltage more up to about 10,000 micro farads.
In any case you will likely need a zener or eqivalent to insure that
the no load voltage is below 3.5 volts and the zener drops 3 volts or
a bit more when lit. Unless specified, none of the component values
are critical, so buy the cheapest available.  Neil

If the voltage to the lit LED, is about 2.8 volts, you can bring it up
to 3 volts by replacing the silicon rectifier with a germainium
rectifier (or grmainium transistor junction) or other rectifier rated
about 0.2 volts forward voltage. If your ac input current exceeds
22ma, you can use a toroidal wound 6 volt ct transformer with two 0.2
volt rectifiers for improved efficiency. This is a full wave circuit
and ct means this is a center taped transformer. A 6.3 volt ct
transformer is likely also ok. Leaving the half the winding of a ct
transformer disconected will lower the voltage to the lit LED and
increase the ac input current, several percent. An MOV rated about 180
volts connected across the ac input after the fuse, may save your LED
in case the power company sends you a voltage spike.  Neil