Hi vp1953,


this appears to be the most popular question on the forum and i'm surprised you don't really see it properly clarified in texts. It has been answered numerous times, and most recently here:

http://www.designers-guide.org/Forum/YaBB.pl?num=1284194476

However, your analysis is not quite correct. You can get higher power gain by power matching directly to the device. Here you have to take into account a more complete model of the transistor's input impedance.


cheers,
Aaron

Hi RFICDEUDE,

Quote:


Let me clarify what i meant by power matching. A pure reactance does not dissipate power and therefore power matching is not possible. However, the input impedance of a MOSFET is not a pure reactance and so in theory power matching is possible. In practice, the quality factor of the input capacitance is too high to match to and so we generally try lower the Q by synthesizing an on-chip resistance (inductive degeneration, resistive termination, resistive feedback, common-gate, etc).

cheers,
Aaron

Your example is incorrect.

Firstly, it is not possible at match to 600j ohms.

Secondly, the voltage gain in your example can be improved significantly by series resonating the gate capacitance. If you series resonate the gate capacitance, then the voltage gain becomes 20dB + 20*log(600/50)

It reality, you are more likely to see an input impedance of -600j + 20 ohm. I put the minus sign because its capacitive. If we write this as an equivalent parallel RC, we get 18 kohm in parallel with -600j ohm. When we match to this impedance, the step up in resistance level will result in a voltage gain of about 25 dB. So you would actually get a voltage gain of 45 dB. So with power matching you will undoubtedly get more gain. However, if you read the links that I posted you will see that this is not the reason that we match to 50 ohm.

Hi Aaron,

Thank you for your lively discussion. There is absolutely no question that series matching -j600 of LNA input impedance will give a substantially larger voltage gain as you have demonstrated. Furthermore my question is not about why 50 ohms (vs 75 or other values) is used which is what the thread you pointed to was discussing - but why match at all for an LNA?

My question is say we have two LNA's
1)one with an input impedance of 50 ohms and a gain of 20db
2) the second one with an input impedance of -j600 and a gain of 20dB

Both give near identical SNR but -j600 impedance has twice as much gain so then why choose the one with 50ohm impedance?  Being able to leave the input impedance at -j600 (or such high values) gives a great degree of freedom (eg no need to have to have a source degeneration inductor etc).

Basically i fail to see the need for matching when without matching i can get nearly same performance.

Where am i mistaken in my reasoning?


ps. it is not possible to conjugate match -j600 of reactance with onchip inductors of low Q, so this would require an offchip inductor which may not be acceptable.

Hi vp1953,


I think I see what you are trying to argue now. You are not talking about compared with power matching, just impedance matching.

In that case I think the points made by rfcooltools are what you're looking for. Apart from that, if you have an off-chip component in between the LNA and the antenna, such as a filter, the transfer function is only correct for the matched case.

For the specific case you are talking about, there is no need to consider travelling waves, and if there are no intermediate blocks, then I don't think there is any need to do impedance matching either.


cheers,
Aaron


Hi rfcooltools,


I don't really follow your example of the 1/4 wavelength t-line.

Quote:


why won't you get twice the signal? From the simulations I have run, you should get twice the signal.


thanks,
Aaron

The question of "Why match an LNA at all?" only matters if the LNA is connected to "controlled impedance" components and systems such as filters, duplexers, transmission lines (RF, SERDES, cable), optical/electrical interfaces (photodiode and laser drivers), etc.

These high frequency or wide bandwidth systems rely on defining a controlled impedance to standardize the interface requirements between different component manufacturers. It also makes it possible to design a system without having to design each component first.

LNA inputs generally interface with transmission lines, filters and/or antennas which all require impedance matched interfaces for the system to achieve the intended performance.

If the output of the LNA does not interface with an external component such as a filter then there is no reason to use impedance matching techniques at the output of the LNA.

There are plenty of other systems that do not require impedance matching (sensors) even when low noise performance is required; however, most of these are low frequency applications.

What are the consequences of not matching in systems using controlled impedance components?
- Not matching antennas will cause a loss of system sensitivity.
- Broadband digital system suffer ISI
- Not matching to a filter can increase insertion loss and distort the frequency response.
- Stability is more difficult to guarantee

Is conjugate matching optimal?
No. As mentioned before, SNR in high frequency narrowband circuits is generally maximized using an impedance different than that of conjugate matching. This is true for antennas too.
For LNAs, as RFCOOLTOOLS said, a systematic design tradeoff can be made to achieve adequate NF and gain. It is possible to tweak the input impedance without changing the noise parameters of the circuit such that the input impedance can be made to be coincident with that required for optimal SNR (minimum NF), but that is getting into too much detail.

I hope this helps clarify why and when impedance matching is needed in LNA design.

vp1953,

Actually the problem again lies with the circuit driving your LNA, (besides the fact that a true open is not possible). Consider two extreme conditions that the source driving your LNA might see depending on tline length and frequency.  to further illustrate picture a source follower or emitter follower driving a very high impedance vs driving a very low impedance which are the two extremes of what the tline andLNA might appear.  In the high impedance case the current leaving the follower is small but very linear.  While the follower driving the very low impedance will have signal at its gate/base while its source/emitter will be an AC short and distortion will be at a maxima.  This might be able to be overcome to some degree by increasing the bias current in the driver to compensate, but then this is really shifting the burden to the source.  

There is also a problem of interference which has been touched upon by rficdude, aaron_do.
For the this concept consider an antenna which can be simplistically viewed as an open at one end and terminated at the other.  The antenna radiates at maximum when there is a standing wave associated with the length of the conductor usually 1/2 wavleength and multiples thereof.  It may not be the best antenna with the ground plane beneath it but it will be pretty good.  This is problematic for two reasons first the signal sourced to you LNA will radiate at some frequency which may be at the desired or even at a harmonic and the FCC will deliver the cease and desist notice to the product.  Antennas also work also receive as well as they transmit and your LNA will be listening to all signals that might be large, like a cellphone nearby or wifi etc.  

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