[AMPS] Conjugate Matching and Efficiency

[Jon Ogden]

> ------------ Original Message -----------
> From: Billy Ward <billydeanward@hotmail.com>
> Date: Thu, 24 May 2001 15:09:04 -0000

> 
> However, think about the method used to determine the value of an output 
> series capacitor.  Do you not take into account the 3db down point and 
> calculate the cap for the proper value based on that.  If the output 
> impedance were not a "lossy" element how would that technique work.
> 

I fail to understand your point.  What do you mean by the 3 dB down point?  If you mean the 3 dB points in a filter (which is essentially what a matching network is), that is something completely different.  I assume that's what you mean so I'll address that.

The 3 dB down point in a filter is typically what is used to specify bandwidth.  That 3 dB down level is basically the level where the magnitude of S21 is 3 dB below that of its maximum value (minimum loss).  At the 3 dB points, half the power that is transmitted at that frequency by the source or whatever, gets passed through to the load or whatever is on the other side of the filter.

So where does the other 3 dB go?  Is it dissipated?  Hardly.  To understand where it goes, one must look at the magnitude of S11 and S22 of the filter.  At the 3 dB point, the values of S11 and S22 are getting large and all of that power is being REFLECTED back towards the source.  In fact for the most part at the 3 dB point, S11 will typically be such that half the power at that frequency won't even get beyond the input of the filter.

What happens to frequencies outside the passband of the filter as well when S21 is say, 30 dB down?  Are the dissipated?  NO.  They are all reflected.  The only dissipation that occurs would be from the inherent non-ideality of the filter elements (Ohmic losses).  The are not absorbed and dissipated as in the sense of a resistor doing it.

The capacitor is not lossy.  It is REFLECTIVE.  There is a big difference.  

Typically, you'll set the values in a tank matching circuit to do multiple things.  You are trying to match the input impedance to the average output impedance of the tube or whatever is driving the tank.  You are also trying to get a Q that will be high enough to attenuate harmonics, but low enough to minimize circulating current.  Since Q is inversely proportional to bandwidth, specifing Q also specifies bandwidth, which by definition will specify the 3 dB points.

I see nothing in there at all about how any of this affects efficiency other than to say that a value of Q that is too high will cause too much circulating current to flow in the tank.  This will decrease efficiency due to the Ohmic losses of the real world components.  In an ideal world, with lossless components, it won't matter.  But this also has nothing to do with the conjugate match and efficiency either.  It's totally unrelated.  A tank circuit with too high of a Q will be inefficient regardless of what is matched to it.

If lumped elements still have you thinking that these circuits are lossy and dissipative, consider the techniques used at Microwave frequencies.  At microwave frequencies, transmission line elements become your matching network components.  An open or shorted stub will be your capacitor, a length of transmission line, an inductor.  So my comments from this morning about the matching network having transmission line characteristics are absolutely correct.  That's what you use at microwaves - transmission lines.  So while all these transmssion lines have characterisitic impedances, they don't act as lossy elements other than their inherent Ohmic losses due to their real world characteristics.  So if you are going to consider that the output impedance of an amplifier or any signal source is figuring into the overall efficiency calculations then you must also take the transmission line into account as well like I did before since the transmission line could really be considered as!
 an extension of the matching network!

I thought about why the efficiency calculation in my "thesis" don't work.  The reason is that the Thevenin and Norton models are designed to tell you about how things work OUTSIDE the model.  Once you try to go inside the model, things fall apart.  This is consistent with what W8JI had said.  The series R in the Thevenin model and the shunt C in the Norton model are INTERNAL to the model.  Therefore it is invalid to try to use them to calculate the efficiency of that model since the model is not designed to do that.  The model is used as a reference to what is going on OUTSIDE.  Yes, we can do things like using the resistances to calculated voltage drops, but that is within the parameters of the model.  Once we start using the model to calculate things inside the model, it doesn't work.  It's basically trying to define the model with the model.  How well would a dictionary work if I used the word I was trying to define in the definition.  For example: "Stop (v): To stop moveme!
nt."  What does that tell me?  NOTHING.  You can't define something in the context of itself.

Hopefully, I understood your point correctly and this was not all for naught!

I am enjoying the discussion and it is challenging and stimulating.  I hope others are benefiting as well.

Regards,

Jon

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