Attached is the schematic of a frequency doubler. It takes a 136kHz input and doubles it to give a 472kHz output. I am not sure how the IC and the two transistors function. The IC is a 74HCT4046 and its data sheet is available here:
https://www.farnell.com/datasheets/66679.pdf?_ga=1.131595913.701848857.1475733716
It appears that most of this IC Is not being used. If you look at the Fig 5 in the datasheet. you'll notice that your signal is going into Pin 14, and coming out Pin 2. The only active 'control' signal is the signal coming in from pin 3. This is tied high on your schematic. Since this feeds, without inversion, into the XOR Gate, the XOR function will always see a '1' on the lower input. As a result, SigIN will always be inverted going out of PC1Out.
I don't know if you're trying to figure out a replacement or not, but I see also no reason why you also couldn't just drop a more common 74HCT gate in there. (adjusting the wiring accordingly) I'd probably use either a 74HCT04 or 74HCT14. You may also be able to get away with a 74HC series instead of a 74HCT series. I'd have to understand a bit better the signal conditions at the input to the gate. If it was on my workbench, I'd build the first part of the circuit, stick a scope on it and make a judgement call.
Since this is a beginner question, I'll add a bit more information for you about the differences in the gates I suggested above. if you already know this, just ignore:
To operate correctly, The 74HCT series needs low voltages to be below 0.8V and high voltages to be above 2.0V. 74HC needs the lows below 1.3V and the highs above 3.7V (at 5V operating voltage, 3.3V is different). It's important to make sure your input thresholds match the signal you're putting into them. Which is why I said above that you could drop a 74HCT series gate in there (since the existing chip is a 74HCT chip), and that you *might* be able to put a 74HC in there - it all depends on the amplitude of the signal out of the doubler.
The Difference between a 74HC*04 and a 74HC*14 is that the 04 requires the signals to transition from low to high quickly or else you will often get stray pulses. A 74HC14 has what is called 'Schmitt trigger' inputs which due to the way they are constructed, will generally help clean up slowly transitioning signals. Because I generally am using an inverter for the purpose of bringing in outside signals to a circuit, I for the most part use the '14 variant pretty much everywhere. I would have to look at the datasheets in more detail to see if for very high frequency circuits there is any meaningful difference in performance between the two - it would not surprise me to find that one or the other does better above a certain frequency.
I can also answer the '50 ohm' resistor question....
The circuit apparently expects you to use a 50 ohm transmission line (i.e. coax, but it's also the connectors on both ends, the pcb etc.). When you put high speed signals down a transmission line you have to be careful to correctly terminate the transmission line. If you don't terminate the transmission line, once the signal reaches the far end, a portion of it will bounce off the far end and return back to the transmitter. I don't want to go into all of the details of how this is bad - but it is. Let's just say that you really want to prevent this.
There are two ways to do this:
1) Provide a *parallel* termination at the far end (aka receiver)
2) Provide a series termination at the near end (aka transmitter)
One could debate the merits of both options. In this case, I'd probably choose to add the 51 ohms at the receiver (class D amp?) just because I could then use a signal generator from the bench and have it be terminated correctly.