Might not be an actual working transmitter, but it does produce a few mW of RF power at 4 MHz using only two LMC555s.
Principle of Operation (see attached simplified schematic):
At lower operating voltages, the flip-flop (TR) input of the LMC555 can be used as an inverting comparator input to control the output of the device. This requires the Threshold (TH) input to be active (high). This circuit applies a DC bias at the switching threshold of TR and superimposes a small AC feedback signal to create an oscillator. An inverted version of the same signal is applied to the second LMC555 to produce two complementary open collector outputs (the device's discharge output). The output is then connected as a standard push-pull RF amplifier. The TH input is used as the enable input to key the transmitter.
This TI design uses Texas Instruments' nanopower system timers, SimpleLink™ ultra-low power wireless microcontroller (MCU) platform, and humidity sensing technology to demonstrate an ultra-low power approach to driving a sensor end node. These technologies enable extremely long battery life: more than 10 years on a standard CR2032 lithium-ion coin cell battery. This TI Design includes system design techniques, detailed test results, and information to get your design started and up to speed.
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