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The input impedance is around 58 ohms (0.7V divided by the current through the collector), which makes it a good match for RF work coupling to coax.
I don't know where you're getting that, but at RF the transistor model becomes
far more complex, and apart from bias, it won't operate anywhere near the same as it does in audio work. I really don't know what to expect from a 2N3904 at say 28MHz (10M band). We had power transistors whose impedance at the base (NPN) or gate (MOSFET) was a fraction of an ohm without any such feedback resistors. (Try matching
that to 50Ω and broadbanding it!) In fact, the input impedance was lower than the output impedance, so the input always had a wider tab than the output. This was at frequencies where you could get around 10dB of gain from them.
Ideally you'd have a network analyzer, directional couplers, attenuators, RF power meters, and all kinds of very expensive equipment if you're going to get serious about RF design; but it really is beyond the hobbyist's budget to go to that extent. The lab I worked in had about $100,000 of equipment
per engineer, and that was almost 25 years ago. If you're only at HF (heaven knows a pull-up resistor in the collector circuit will sure limit the frequency!) and really know what you're doing, you could probably jerry-rig a significant part of it while getting a few things from the electronics swap meets or eBay. Still, it would be good to sneak it into a decent lab to at least get some calibration data on your many pieces of equipment.
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why would Rf = 70K?
Let's say you want the collector to sit at 6V, and the base will sit at .7V. The difference is 5.3V. Further, say your Vcc is 12V, so (12V-6V)/270Ω=22mA. Hmmm... 22mA*6V means a power dissipation of 133mW-- definitely enough to warm up the 2N3904. Oh well, be that as it may, let's say the β is 100 under the conditions of interest (you better measure it though, because you have no means of stabilization on that circuit!), so the base current is 220µA. The 5.3V above divided by 220µA is 24K. Hmmm... better get a higher-gain transistor if you're set on 70K. Of course a little simple algebra now can turn it around to get whatever variables you want to solve for to make it work as desired. Keep in mind though that temperature has a large effect on the behavior of the transistor, and there can be big differences particularly in β from one transistor to another of the same type, especially if they're from different wafer lots.
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and the fact that it taps the collector output means you can not think of the transistor as a variable current source anymore (with or without a resistor from base to ground), for now your output voltage is the result of a simultaneous equation, thanks to the fact that your transistor's bias (that which should be most stable) is now predicated on the amplified signal (that which is most variable).
Going back to the case of an audio circuit (to make things simpler), the base impedance is so low compared to the values of the Rf and base-to-ground resistor that it's not really an issue. Although the transistor is more-or-less a variable current source (it's not ideal though-- a curve tracer won't show you flat curves), the feedback mechanism turns the whole circuit into a current-controlled voltage source, the controlling current being the AC signal current coming in through that input capacitor.