24vAC to 9vDC: half wave regulator input?

[npomeroy]

I'm making an irrigation control system with 24VAC valves, 12vDC relays and 9vDC Arduino controller.

When I cut the 24vAC "in half" with a single power diode and smooth with a capacitor I read 40vDC.
I've bought a series of voltage regulators hoping to cascade down the voltage (all TO220)
MC7824CT (24v out, 40v max input)
LM10851T-12 (12v, 3A out, datasheet says 18v max input
LM7809

Both the 24v and 12v regulators get hot to touch when running with no load. (EDIT correction - it is drawing 80mA when driving Arduino with 9v)
I could add heat sinks.

But would the 24v regulator perform OK if I omitted the capacitor, i.e. used un-smoothed half wave input?

In any case this seems a clumsy setup (I thought I'd simply get 12v with the single diode). Perhaps I'm better to go to a separate power supply but that's clumsy in a different way.

Edit again... If it's "too hard" I'm tempted to replace the 24v transformer with a multi-tapped one to get the lower voltages.

 

[Harald Kapp]

But would the 24v regulator perform OK if I omitted the capacitor, i.e. used un-smoothed half wave input?

Definitely not. The output voltage will follow the input for voltages below the set output voltage.

My suggestion: get a step-down regulator which can be as cheap as 3 USD or less.

 

[duke37]

It is much kinder to the transformer to use full wave rectification. If using a reservoir capacitor, the voltage will not be much higher than half wave rectification.

The 12V relays can run on rectified AC with no capacitor. Put a suitable resistor in series with each relay and include a flywheel diode acoss the relay.

A diode from the rectified supply charging a capacitor will give a smoothed supply for the arduino regulator.

 

[kellys_eye]

Use a switching (buck) regulator - more efficient (i.e. less heat) and straight from (hi)volts input to (needed)volts output with subsidiary linear regulator(s) for the incidental output voltages.