OK, here's a circuit description for the non-coded infra-red remote on/off controller design in post #16.
There is an error in the schematic in post #16: in the receiver circuit, the CD4017BE IC is identified as U1. It should be marked U2. (U1 is the TSOP1738 infra-red receiver device.)
The Transmitter:
U1 is a CD4069UBE hex inverter device. You MUST use a part with a "U" in the suffix, which indicates that the gates are "unbuffered". An unbuffered gate (containing only two MOSFET devices) is needed to make the oscillator work properly with those component values.
The first gate, on pins 1 and 2, is used as an inverter biased into its linear region by R1, with feedback through X1, a 455 kHz ceramic resonator. This arrangement is known as a Pierce oscillator and is widely used.
The output on pin 2 is buffered by another gate and comes out on pin 12, where it feeds U2, a CD4024BE ripple-carry binary counter, which divides the frequency down using cascaded "T"-type flip-flops.
D1 and D2 form a diode logic AND gate that detects when a count of 1100 binary (12 decimal) is reached, and resets U2. This causes U2 to divide by 12 and produce an output signal on pin 6 which is 1/12th of the 455 kHz clock frequency, i.e. 37.91667 kHz, and has a duty cycle of 33%.
This signal is inverted by another inverter gate in U1 then fed to the inputs of the three remaining inverters, whose outputs are also commoned together. This gives a combined output impedance three times lower than a single gate, which can drive more current through R3.
The signal at pins 4, 6 and 8 is a rectangular wave with 33% duty cycle. R3 feeds this signal into Q1's base with a current of about 8 mA.
Q4 drives LED1, the infra-red-emitting diode. Q4 should have a reasonably high gain so that it saturates well with the limited base current available; I've suggested a BC337-40 which has a current gain of 400 or more, and a maximum collector current of 800 mA (500 mA for NXP's version).
The intensity of the infra-red light emitted by LED1 is roughly proportional to the current that flows through it, which is set by R4 and can be calculated using Ohm's Law, I = V / R, where I is current in amps; V is the voltage across R4, in volts, and R is the resistance of R4, in ohms.
The voltage across R4 is equal to the battery voltage minus the LED's forward voltage (typically about 1V for an infra-red LED, but look on the LED's data sheet), minus about 0.3V for the collector-emitter saturation voltage of Q1.
You can increase the current (by reducing R4) if you find the remote control range isn't enough, but make sure you don't exceed the manufacturer's recommended maximum current for the infra-red LED you're using. The circuit pulses the LED at a duty cycle of 33%. The data sheet for the LED should have a graph that tells you the maximum allowable current for the LED at various duty cycles.
Ohm's Law can be rearranged to R = V / I so you can calculate the correct resistance for R4 from the other values.
The specified resistance, 100 ohms, gives a current of (4.7 / 100) = 47 mA, assuming an LED forward voltage of 1V (6V battery, minus 1V LED voltage, minus 0.3V Q1 saturation voltage, leaves 4.7V across R4).
These calculations assume a new battery. The LED current will drop as the battery runs down.
The infra-red LED, LED1, should have a peak infra-red light wavelength of 840 nm, because that's where the TSOP1738 is most sensitive.
Don't try to power the circuit from a smaller battery such as button cells. It won't last long with button cells, and it may not work properly because of the high current pulses that it draws.
C3 and C4 are decoupling capacitors, 100 nF (also known as 0.1 µF), ceramic. They must be connected as directly as possible between the power pins of their relevant ICs.
C5 is a decoupling and reservoir capacitor. It provides extra current during times when LED1 is illuminated, and reduces noise on the supply rail. It must be rated for 10V or higher. This power supply noise is also isolated from U1 and U2 by R5.
The Receiver:
The receiver needs a 5.0V power supply that is rated to provide at least 0.1 amps.
U1, a Vishay Telefunken TSOP1738, is an integrated infra-red receiver and demodulator that detects infra-red light modulated at about 38 kHz. It pulls its output low when this light is detected.
R1 and C1 isolate U1 from noise on the power supply rail.
When light is detected, C2 charges up via R2 and Q1 turns ON, pulling pin 14 of the CD4017 (incorrectly labelled U1; it should be U2) high. When the infra-red light stops, the internal weak pullup resistor in U1 discharges C2 slowly through R2 and Q1 turns OFF.
This quick response to light and slow response to no light is needed so the circuit can be used with a standard infra-red remote control transmitter which transmits its modulated infra-red light in bursts. The transmitter shown here transmits a continuous stream of modulated infra-red light, so it should not cause misoperation of any other remote-controlled devices. However, the receiver will respond to any infra-red remote control.
U2 (mislabelled U1) is a CD4017BE decade counter/divider IC. It has ten outputs; only one output is active at a time. It responds to rising edges on pin 14 by advancing to the next output.
Output Q2 (pin 4) is connected to the Reset input (pin 15) so when the count advances from 1 to 2, the device resets immediately. This means that on every rising edge on its clock input, it alternates between count 0 and count 1.
The count 0 output on pin 3 drives LED2, a red LED that lights when the appliance control is OFF. This LED and its current limiting resistor R4 can be omitted if they're not wanted.
The count 1 output on pin 2 drives LED1, a green LED that lights when the appliance control is ON. It also controls the appliance via Q2.
When U2 pin 2 is high, current flows through R6 and forward-biases Q2. This applies 5V across the coil of K1, the appliance control relay.
K1 is shown as a DPDT type (two sets of changeover contacts). The types listed, EC2-5NU and V23079A2001B301, are common, small, cheap, and available from Digikey. Their coil currents are 28 mA which is fairly low for a 5V coil. But their contacts are rated to switch only 2 amps, and that's into a non-inductive load.
If you want to switch something bigger, or DC at more than 28V and 2A, you will need a bigger relay. Any relay that has (a) a coil rated for 5V DC, and (b) a coil current of 50 mA or less, will work. Here are some suggestions.
Omron G6M-1ADC5: can switch 3A.
Omron G5T-1ADC5: can switch 5A. Coil current 40 mA.
Panasonic ALQ305: can switch 10A. Coil current 40 mA.
Omron G5Q-1ADC5: can switch 10A. Coil current 40 mA.
Omron G5Q-1A4DC5: can switch 10A. Coil current 40 mA.
Panasonic ALE75B05: can switch 16A. Coil current 40 mA.
Panasonic ALE75F05: can switch 16A. Coil current 40 mA.
C1 and C3 are decouplers; see the notes for C3 and C4 in the transmitter.
Q2 can be any of the types listed. If you're already getting a BC337-40 for the transmitter, you might as well use one here too.
D1 protects Q2 from damage when Q2 turns off and the supply to the relay coil is interrupted, by clamping the back EMF voltage from the relay coil. It is specified as 1N400x. This means any member of the 1N400x series, from 1N4000 to 1N4007 inclusive.
C4 is a power supply smoothing capacitor, like C5 in the transmitter. It must be rated for 10V or more. C2 has less than 1V across it.