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I found some FM transmitter circuits with the MAX2606 VCO.

Example: MAX2606 transmitter

Can I replace R1 with the DAC output from an AVR microcontroller? Or can I connect the DAC directly to Pin 3 of the MAX2606?

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    \$\begingroup\$ Note that AVR chips don't have real DACs, but PWM generators. To make an ADC out of a PWM signal, you will need at least some external components. Or even better, a dedicated DAC chip. \$\endgroup\$ – Fritz Feb 13 '17 at 13:58
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Can I replace R1 with the DAC output from an AVR microcontroller?

Yes you can but be aware of noise on the output of the DAC especially when changing DAC values - you get a bit of capacitive coupling from the clock and this might require a bit more filtering than just the 270 ohms and 2200 pF will bring about.

For this reason, it's not generally recommended to directly couple a DAC output directly to the TUNE input.

ADDED SECTION Given that the "so-called" DAC output may be PWM output with possibly some filtering, I would advise to make any filtering as decent as possible. The PWM frequency needs to be kept as high as possible and you will probably need at least a 2nd order low-pass filter with a bandwidth of sub 10 Hz (or better).

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Can I replace R1 with the DAC output from an AVR microcontroller? Or can I connect the DAC directly to Pin 3 of the MAX2606?

Yes and Yes.

all the chip cares about is a voltage there. doesn't matter how that voltage is generated.

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    \$\begingroup\$ AVRs don't have a real DAC, only PWM outputs. So they do not generate "a voltage", but rather "a signal which rapidly oscillates between VCC and GND". This is almost certainly not going to work as an input for a VCO. \$\endgroup\$ – Fritz Feb 13 '17 at 13:56
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    \$\begingroup\$ Yes, but as mentioned above, a DC voltage plus residual noise will cause problems, probably unwanted modulation in an FM transmitter. And in any way, such an assumption is only valid if the output impedance is low and constant (this is often an issue with DACs!, and if the input impedance is high and constant). \$\endgroup\$ – rackandboneman Feb 13 '17 at 13:59

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