I'm trying to optimize an impedance transformer for the output of a narrowband RFPA. Let's presume I have an antenna impedance ZA and the output impedance of my amplifier is Zamp. I want my impedance transformer to present the optimum load impedance Zol to the amplifier. Zol, is not a conjugate match of Zamp; it's something different in order to maximize efficiency as opposed to power transfer.
Obviously there are tons of possible ways to implement this impedance transformation, but what if we also care about the impedance seen by the antenna port looking back towards Zamp through the transformation network (we'll call this Zs)? Are there any theoretical constraints on what that impedance Zs can be given ZA, Zamp, and Zol? Assuming a lossless, reciprocal transformation network, but with no constraints on the construction of the network.
Thanks in advance.
Makes no difference, if you now required impedance value that you want to present at the radio-interface is it the value you should use for conjugate matching. Simplest can a impedance matching network be designed by measuring impedance near radio interface and calculate a correcting network that results in a conjugate match for the impedance that results in optimal efficiency.maximize efficiency as opposed to power transfer.
Have not seen any lossless transformation IRL, and if it is a question about system efficiency, is it often an important factor.Assuming a lossless, reciprocal transformation network,
Believe me, I know for certain that a conjugate match is not optimal for me. My switchmode PA gets best efficiency when my reflection coefficient is between 0.5 and 0.75. And I also desire a large reflection coefficient presented to the antenna port. Sounds strange, but my application is not typical.Makes no difference, if you now required impedance value that you want to present at the radio-interface is it the value you should use for conjugate matching.
When calculating optimal system efficiency can not a TX-circuit efficiency be isolated from antenna efficiency. If TX impedance is offset from impedance resulting in lowest reflection factor, do it also cost dropped antenna efficiency due to not optimal antenna impedance matching. Lees antenna efficiency must be compensated by increased TX power to reach same amount of TRP, if TRP is a measure of system efficiency.
My bandwidth requirements are quite narrow, about a thousandth of my carrier frequency. The matching network itself doesn't have to have any specific frequency response (the antenna itself is quite narrowband). And of course I'm not expecting perfect tolerances or zero losses, but as of now I'm only asking what's achievable at a single frequency with ideal components, so that I know if my desired Zs is possible to achieve or not in theory. If theory says it is possible, then I should move on to consider practical matters. If not then I'd be wasting my time, that's why I'm keeping the question simple.If you consider only "theoretical" constraints, bandwidth is essential. It's also the principle constraint of electrical small antennas, as you probably know.
For practical matching networks, component tolerances should be considered besides losses.
You can calculate mutual dependency of the s parameters of a lossless, reciprocal two-port network based on the general properties of s parameters. There are no other constraints for an "ideal" impedance matching network as far as I see.Are there any theoretical constraints on what that impedance Zs can be given ZA, Zamp, and Zol?
I can't follow the considerations. Γ=(ZL-Zs)/(ZL+Zs) is correct with no loss of generality.ah apparently the equation Γ=(ZL-Zs)/(ZL+Zs) is not correct in general. Using Γ=(ZL-Zs*)/(ZL+Zs) seems to be consistent with |S11|=|S22|.
In my application I'm not dealing with cable or transmission lines, at least not at the moment, so I don't really have a defined Z0 (except as an arbitrary reference impedance I can choose, I suppose). I was under the impression that reflection coefficient and S11/S22 were, by definition, equal. And if that formula for reflection coefficient is correct in general, then that means that S11 and S22 should also be defined by ZL and ZS at any node in the network, right?I'm not completely sure about your calculation. The problem might be that you are terminating both ports with Z ≠ Z0 but still assume, that S11 and S22 are representing the input impedance.
What exactly is Z0, in this case where all my impedances are different?But you must put S21 and S12 in the calculation to determine the reflection factor at one port if the other port isn't terminated with Z0.
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