The Dark Side of the Conjugate Match

Discussion in 'General Technical Questions and Answers' started by KL7AJ, Mar 12, 2010.

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  1. K7JBQ

    K7JBQ Moderator Volunteer Moderator QRZ Page

    Ah, I thought women were always looking for the "perfect match."

    You mean "Mr Right" is not the same as "Mr. 50 Ohms?"

    73,
    Bill
     
  2. WA9SVD

    WA9SVD Ham Member QRZ Page

    Nah! It's a form of torture imposed upon Latin students. Just don't ask what "declension" is. It's too horrible to describe on the "Zed." ;-)
     
  3. WA4OTD

    WA4OTD Ham Member QRZ Page

    The match required for lowest noise figure is also normally slightly off conjugate match.
     
  4. W8JI

    W8JI Ham Member QRZ Page


    For those learning about the conjugate match, nearly all of the above is incorrect.

    As W5DXP correctly points out, there is no rule that the real part of an impedance has to be a dissipative resistance.

    Many years ago when the endless argument between Bruene and Maxwell was in full heat, I measured dozens of amplifiers. A deep class C amplifier, when tuned for maximum efficiency, looked almost exactly like a conjugate match (doing a load-pull). At that point the efficiency was something like 80%. This was not a special "trick" amplifier, it was a modified DX100 Heathkit with high bias on the grids (short conduction angle) and third harmonic resonators in the anode and grid to sharpen transition slope of the plate current waveform.

    Of all the transmitters and amplifiers I tested, the one universal occurrence was they reached peak efficiency very close to the point where they also looked like a conjugate match. At that point, efficiency could easily be well over 50%.

    The systems did not need to operate with a conjugate match, but doing so certainly did not limit efficiency to 50% or less!!!! I am absolutely positive my measurements were good, because I verified them several ways and tested quite a few transmitters and amplifiers.

    Automotive alternators, if tested with constant field levels (no feedback from regulator), behave the same way. A load pull will show they deliver maximum possible load power when conjugately matched, and the efficiency can be more than 50%.

    If anyone tells you efficiency has to be 50%, they probably do not fully understand impedance and the fact that the real part does NOT have to be a resistor or dissipative resistance. :)

    Even the rules of the theorems clearly state the theorems cannot be used to tell us anything about what goes on the source so far as efficiency, and that the theorems cannot be used in the non-linear portion of the system. (This is not transfer ratio linearity, but rather the impedance linearity.) The output systems in our transmitters and amplifiers do not have to be conjugately matched, and often are not conjugately matched, but to have peak efficiency and maximum power transfer we better have it damn close to a conjugate match!

    73 Tom
     
  5. W5DXP

    W5DXP Ham Member QRZ Page

    Perhaps it would be appropriate to review the three separate definitions of impedance from The IEEE Dictionary:

    "impedance -

    (1)(A) The corresponding impedance function with p replaced by jw in which w is real. Note: Definitions (A) and (B) are equivalent.

    (1)(B) The ratio of the phasor equivalent of a steady-state sine wave voltage ... to the phasor equivalent of a steady-state sine wave current ...

    (1)(C) A physical device or combination of devices whose impedance as defined in definition (A) or (B) can be determined. Note: This sentence illustrates the double use of the word impedance ... Definition (C) is a second use of "impedance" and is independent of definitions (A) and (B)."

    Only the "physical device", i.e. an "impedor", necessarily dissipates power. All up and down a transmission line with reflections, the ratio of voltage to current is an impedance that does not dissipate power. The ideal resistive characteristic impedance of a transmission line doesn't dissipate power. Why is it so hard to accept the fact that an RF source impedance may have a non-dissipative resistive component?

    We were all told in our EE classes that an equivalent circuit's internal dissipation doesn't necessarily bear any resemblance to the dissipation in a real world source and should only be used to predict external conditions.
     
  6. WB2UAQ

    WB2UAQ Ham Member QRZ Page

    A good signal generator is a good example a 50 ohm source. An output leveling circuit keeps the voltage constant just a head of a series 50 ohm RESISTOR. Keeping the voltage constant simulates an ideal voltage source. The series 50 Ohm resistor forces the circuit to be a "50 Ohm source". As Eric pointed out at the beginning the energy is divided equally between this source resistance and the 50 ohm load resistance at max power into the 50 OHm load. My point is that our transmitters are not configured like this at all. I view them as just energy sources designed to deliver a certain amount of power into 50 ohms or whatever impedance it was designed to drive. Never think of our transmitters as 50 ohms sources in the Thevenin equivalent sense.
    As a side note, a good sig gen can become a 600 ohm source just by adding a 550 ohm resistor in series with its output or a 75 Ohm source if 25 ohms is added in series, etc..
    73, Pete
     
  7. K7FE

    K7FE QRZ Lifetime Member #1 Platinum Subscriber Life Member QRZ Page

    I must agree with Tom and Cecil. A conjugate match may certainly achieve higher efficiencies than 50%. Most of the transmitters that I have designed over the last 40+ years have had efficiencies much higher. MOSFET designs using Class D amplifiers have efficiencies approaching 90%.

    Transmitter efficiencies are largely determined by the operating class, then comes design and match. A poor design and/or a poor match will reduce the "expected" efficiency for a particular class of amplifier. One should always attempt to provide a conjugate match, but "close" is what we usually achieve. Close works fine with little contribution to losses and resulting output power. A bad design.......well is just bad and may have many undesired effects. Efficiency degradation is one of them.

    The 50% loss in a battery while powering a load statement was dis proven over 100 years ago. (I think by Edison.) To improve the DC efficiency, one must only find a battery with a lower internal Resistance than the load. That way less power is dissipated in the battery and more in the load.........thus higher than 50% efficiency.

    73,
    Terry
     
  8. W8JI

    W8JI Ham Member QRZ Page

    Pete,

    No one said or implied we cannot make a source that has a dissipative resistance dominating source impedance.

    That being said, amplifiers with conduction angles shorter than 360 degrees are not signal generators though large pads. Neither are power limited sources, like an alternator with fixed levels of field excitation or a fixed level of energy driving the shaft.

    There are countless examples of systems that have a conjugate match with efficiency greater that 50%, thank goodness!!! A conjugate match absolutely does not mean efficiency is 50% or less.

    73 Tom
     
  9. WB2UAQ

    WB2UAQ Ham Member QRZ Page

    Tom,
    I was thinking about bringing this up with my last remark in regard to sig generator output impedance. This might have been covered earlier by Eric as well. The topic being the impact of the source impedance when making accurate SWR or RL or Z measurements using directional couplers.
    This might also help explain why there are concerns about why different SWRs can be measured in an RF path depending on where the SWR measurement is made in the path.
    If the effective source impedance of the sig generator (or one our of amateur band transmitters) and the SWR measuring instrument following (SWR looking back into the SWR meter and thru the SWR meter into the transmitter) do not have a good match to the transmission line, re-reflections will cause errors. The higher the SWR becomes on the line the greater the error becomes because the reflected signal is re-reflected by this poor match. However, if the SWR is very low, the reflected signal is very low and the re-reflections are small making the error small. In the end, if the effective match is good to begin with, the re-reflections are very low for even high SWR's so the accuracy of the measurement is much better. This is why the SWR measurement uncertainty is a function of the SWR being measured and the effective source match. So, with a transmitter having no where near the ideal source impedance, higher SWR measurements (with higher re-reflections) will be messed up and will change depending on where the SWR meter is placed in the transmisson line. Hopefully I explained this well enough and I didn't make a mess of it:) This is all in some famous app notes that HP published and supplied with their early vector and scalar network analyzers before computers made it possible to calibrate out the errors due to directivity and source match and so forth.
    I often thought about this when testing an antenna with an actual transmitter (with a non-ideal source impedance)and not a good sig gen. I would think this would impact measurements made even with a Bird 43 watt meter as it uses a directional coupler scheme. 73 Pete
     
  10. W5DXP

    W5DXP Ham Member QRZ Page

    Steady-state SWR = [1+SQRT(Pref/Pfor)]/[1-SQRT(Pref/Pfor)]

    The source impedance may indeed affect the magnitude of Pfor but the source impedance in no way affects the ratio of Pref/Pfor which is dictated by the mismatch at the load.
     
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