Achieve 50 ohm input impedance in amplifier

[kronos]

Hello,

I have been experimenting with discrete BJT RF amplifiers, and have one based on MPSH10 with a high input impedance Zin.
If I want to get a 50 ohm input impedance, I could put a feedback resistor between output and input, as in this circuit:



As I have understood, applying Miller´s theorem this is equivalent to an impedance of \$Z=\frac{Rf}{1-Av}\$ in parallel with Zin. If the gain Av is negative (inverting amplifier) and I choose Av and Rf conveniently, this Z can be 50 ohm, which in parallel with Zin is still 50 ohm.

Indeed, if I do this in LTspice, I get the following input impedance of the amplifier:


My question is why would I do this (taking into account that the input impedance soon deviates from 50 ohm, as seen above, and this method reduces the gain, as there is a second impedance in parallel with Rl). Instead, I could simply put a 50 ohm resistor at the input, in parallel with Zin, with no gain loss and the following resulting input impedance:


I fail to see the problem in this second simpler method. The input power would be wasted in this input resistor, but this is also the case in the feedback resistor method, I think. What do you think?

[TimFox]

Properly done, shunt feedback to reduce the input impedance contributes less resistor noise than does a single 50 ohm resistor at the input.
However, in practice it is easier to obtain a reliable high input impedance (>> 50 ohms) over a broad frequency range and then reduce it to a constant 50 ohms with a discrete resistor.
Adding a resistor to a circuit always decreases the signal/noise ratio.  That is why RF applications often use a matching network (broad-band transformer or tuned circuit) at the input to connect a 50 ohm source to the amplifier.

[kronos]

OK, if I understand you correctly, the shunt method is preferable due to the lower noise.
In my case, I want a broadband amplifier, so I cannot use an LC network. A transformer is an option, but I do not have any (and they are bulkier, but that should not be a problem).
So I am left with the two resistor methods. The shunt resistor method on the other hand only gives me 50 ohm in the low frequency range (see LTspice results). I think I prefer the 50 ohm resistor at the input.

[TimFox]

Done properly, the feedback resistor should have lower noise and waste less power, but the open-loop voltage gain of the amplifier is frequency-dependent (including its phase angle) and that directly affects the “Miller impedance” at the input.  If the impedance looking into the input is critical, the direct connection of 50 ohms is preferable.
Transformer coupling (broadband or tuned) is used to optimize noise performance from a microphone, antenna, or other generator with a source impedance.  Broadband RF-range low-power transformers are readily available in reasonable sizes (see MiniCircuits Lab catalog).  Good audio transformers are larger and more expensive. 
The basic limits to low- and high-frequency performance of broadband transformers are the magnetising inductance and leakage inductance, respectively, along with parasitic capacitances.

[Terry Bites]

If you don't limit the bandwith of your amplifier you will incur more noise regardless of terminator configurations. Unless you specify a measurement bandwith, NF is undefined.

[TimFox]

Technically, noise figure (NF) is a function of frequency, but not of bandwidth.
Signal-to-noise ratio (SNR) is a function of bandwidth.

[mawyatt]

There was an interesting discussion long ago with the late Barrie Gilbert about the "limits" of electronic amplifier linearity. Recalling as best I can, the discussion centered around the input impedance of the amplifier being influenced by the input signal itself.

Some amps are more influenced than others, but all amps are influenced in some way and thus the input characteristics become a function of the input signal. This creates a linearity limit right at the amp input before anything else takes place, because the input signal at the amp input is changed by the amp input characteristics (think of a simple voltage divider), and without a perfect zero impedance input source, the signal suffers a fundamental non-linearity, somewhat self-inflicted.

The discussion also involved Gilbert's MicroMixer which exhibited "gain expansion" rather than the usual "gain compression" over certain input signal levels where the input impedance is bounded within a range of input signal levels. We utilized these MicroMixers in a number of custom chips in IBM's Silicon Germanium BiCMOS processes (7hp thur 9hp).

Edit: Spelling

Best,

[TimFox]

This is an example of a non-linear common-mode effect, which can include the “Early effect”, where the change in collector-base voltage caused by the input voltage change modulates the input impedance of the transistor.  Common approaches to reduce the effect in amplifier circuits include a bootstrapped cascode, where an active circuit maintains the collector-emitter voltage constant as the base-ground voltage changes.
Since the non-linear effect actually affects the voltage at the input terminal (with finite source impedance), it cannot be reduced by negative feedback.

[mawyatt]

Even simpler, gm!!

Best,