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My group made an RCA video/audio to RF modulator for a school project. The video is a NTSC composite video signal. Here is a clip of our tv receiving the output of the project on NTSC channel 2:

https://drive.google.com/open?id=1-1xRHI8razjYvvptTsPsPBHt8T0z-yi5

In the video, we use an usb-to-hdmi adapter from Raycue, a hdmi-to-composite video/audio adaptor from Ozvavzk, and a tv from Thomson Consumer Electronics (model 19GT241).

I made measurements of our audio and carrier signals using a Siglent SDS 1202X-E Oscilloscope and a $12 active probe (which is listed on eBay as "RF Active Probe 0.1-1500 MHz").

I measured the audio carrier signal to be 55.2 MHz and I measured the video carrier signal to be 59.2 MHz. I did a FFT of the two signals - the audio's bandwidth looks narrow like a dirac-delta function and the video's bandwidth is about 500 KHz wide.

According to the "Pan-American television frequencies" article on Wikipedia, if we are to transmit on channel 2, then our audio and video carrier signals should be tuned to 59.75 MHz and 55.25 MHz, respectively. I can't find information that supports the carrier frequencies of our project are alternative ones for channel 2. Why is our tv playing audio and video if the carrier frequencies in our RF project are not tuned according to the article?

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The old analog signal TVs had a wide frequency range allocated to each channel. Channel 2 for instance occupied everything between 54 MHz and 60 MHz.

Because of effects of temperature and other conditions on the hardware (e.g. resistors and capacitors), the transmitter and the receiver could drift slightly from the exact frequency. To compensate, the TV had a "fine tuning" control allowing one to adjust it to match the actual frequency. The set you were using either had AFT (Automatic Frequency Control), or you manually used the fine tuning yourself.

Wikipedia's "Pan-American television frequencies" has this table, showing that your 55.2 and 59.2 were well within the channel 2 frequency range:

VHF low-band

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