Why dB or dBm vs Volt/Volt?

Discussion in 'Radio and Communications' started by PRS, Jan 8, 2010.

  1. PRS

    PRS Thread Starter Well-Known Member

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    I do not understand why matching resistances is so important in rf applications. Why not just consider each function as a module and give it high Rin and low Rout? By function, I mean such systems as an audio amp, an if amp, an rf amp. I'll sure appreciate your input.

    Also, I worked briefly for a company that made frequency synthesizers. We used dBm there. Why not dB? Why not gain expressed in V/V?
  2. rjenkins

    rjenkins AAC Fanatic!

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    Transmission lines need matched source and load resistance to avoid signal reflections from the line ends.

    When cables or connections are a miniscule fraction of a wavelength (as in audio), most consumer manufacturors don't bother (though professional audio gear tends to be matched at 600 Ohm, as do telephone lines which can be rather long).

    As the cable or transmission line gets to a significant part of a wavelength, mismatches cause signal distortion an possibly corruption. Take a look at the termination and matching requirements for the SCSI bus system for an example.

    At RF, mismatches cause standing waves on cables which can cause extreme problems and damage equipment.

    Another reason for matching is down to power transfer efficiency:
    Imagine two resistors connected in series from a signal source to ground; the first from the signal is the source resistance, the second, to ground, the terminating resistor.

    For any given signal level or voltage, the maximum *power* transfer (as in V * I) to the load resistor happens when the load impedance is equal to the source impedance.
  3. bertus

    bertus Administrator Staff Member

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  4. PRS

    PRS Thread Starter Well-Known Member

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    Thank you very much for this reply to my inquiry. I've understood the maximum power transfer stuff, but not the SWR. I'll let you know what I am doing that brought this up: I'm designing and building a 455KHz IF amplifier as a generic lab module. From what you said, I should have an input impedance of 50 ohms and an output impedance of 600 ohms.

    The rf amp and mixer feeding this IF amp should have an output impedance of 50 ohms and the detector and audio amp should have an input impedance of 600 ohms. Is this right?

    To get the 50 ohm input impedance to the first IF stage we have a CE amp with an input impedance of 2.5 Kohm at 1 mA. Then probably about 2.2Kohm with the base bias resistors included. To get a 50 ohm input I should then use a step up transformer such that this 2.2 kohm looks like 50 ohms to the input?
  5. PRS

    PRS Thread Starter Well-Known Member

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  6. someonesdad

    someonesdad Senior Member

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    dBm means a power ratio relative to 1 mW. You could certainly use dB also, but you just have to explicitly state what the ratio is referred to; otherwise, it's ambiguous.

    And there's nothing wrong with expressing gain as a dimensionless number. Engineers and scientists who work with numbers that range over pretty big ranges often reduce the scale to a logarithmic one just to work with more "reasonably-sized" numbers. Besides power, voltage, and current ratios, earthquake magnitudes are another familiar logarithmic scale.
  7. rjenkins

    rjenkins AAC Fanatic!

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    PRS:
    The simplest analogy for impedance mismatch or SWR is to imagine a single ripple travelling down a canal with perfectly parallel sides.

    Any sudden change of width (= impedance) causes reflections which both affect the wave and bounce back toward the source.

    If you have a good high frequency 'scope, you can build a simple time domain reflectometer; this is a great device to literally look at impedance along a transmission line. All it consists of is a medium frequency oscillator with a good buffer and a source resistor. I used a little crystal osc module with a built-in divider. Something with an output in the 10 - 100KHz range should be OK. As a buffer I used all the sections of a 74ALS244 in parallel, then a 50 ohm resistor from that to the output terminal (and plenty of decoupling on the 5V supply).

    Put both the x10 scope probe and the cable (or string of cables) on the output terminal and you will see a graphical representation of impedance against time.

    Back to your I.F. amp:
    The stage input resistance is high enough so just putting a 51 Ohm resistor across the input and ground, then a cap to the base cct should give a decent match.

    Typically, I.F. transformers are double wound and tapped, allowing matching via the transformer. If you want to use transformer matching rather than resistive, you want about 6:1 or so, as impedance ratio is the square of the turns ratio.

    If the output is still RF, you could also use a tapped IF transformer to get an appropriate output impedance.

    If it's audio, you could use a 600 Ohm audio transformer in the output stage, this has the advantage of eliminating the common ground and removing hum loops. The transformers from 56K PC modems are 600 Ohm and rated to stand some DC current, so they can be used directly in the collector circuit of an amp stage. These 56K modem transformers are cheap and readily available, or just use one from a scrap modem.
  8. PRS

    PRS Thread Starter Well-Known Member

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    Thanks for the advice, all of which seems sound. The 51 ohm resistor at the base of the first IF stage is just too simple to be real, but I'll try it. In matching the 2nd to the 1st and the 3rd to the 2nd stages I plan to use singly tuned transformers with some sort of matching network at the output for 50 ohms. Is this reasonable in your opinion or is there an easier or better way? Remember this is a general purpose amp for the lab.

    Also, what is the easiest and most economical way to control the gain? I'd like to keep it simple with just 3 stages.

    I sure appreciate your help. :) Thanks again for the advice you've given me so far.
  9. PRS

    PRS Thread Starter Well-Known Member

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    dataman, I sure appreciate your response. I can see I have some serious homework to do in order to really get a grip on this. Until getting into radio recently my whole approach to amplifiers was voltage gain rather than power gain. I was also blissfully ignorant of SWR, though I had encountered the term without actually worrying about it.

    Thanks for the info. :)
  10. KL7AJ

    KL7AJ E-book Developer

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    Hi Paul:

    There are indeed some R.F. applications where maximum power transfer is not the main goal, in which case treating the generator as a voltage source makes sense. As long as the transmission line is less than about .1 wavelength, SWR is not particularly an issue. (I posted a rather lengthy treatise on AAC not long ago called, "SWR Meters Make You Stupid.")

    As far as dB is concerned, when you're expressing very large power (or voltage) ratios, dB keeps the numbers more manageable. Also, it makes most calculatons a mere addition problem. :)

    Ultimately, ALL dB measurements are power measurements, even if you're deriving them from VOLTAGE ratios. This is why, if you DO you voltage to calculate dB, it MUST be the same impedance on both sides. If you violate this rule, you can show that a step up transformer gives you POWER GAIN, which we know is impossible! So you're always safer dealing with power. :)

    Eric
  11. PRS

    PRS Thread Starter Well-Known Member

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    Hello, Erik!

    While I was playing with the math I discovered that from this equation...

    PG = A^2*(Zin/Zout)

    ... where A is the voltage gain, that I would maximize power gain by making Zin as large as possible and Zout as small as possible. And this idea seems to violate the theorem that power to the load is maximized when Zin = Zout! It struck me that the power gain, PG, was meaningful only when Zin = Zout. I could be wrong, of course.

    By the way, how do Real Men measure voltage without a voltmeter? Are you talking about licking your fingers and experiencing the voltage for yourself? When I was stationed at Ft Bliss, we'd cross the river into Juarez and get drunk in a bar. Unfailingly a man would come in with a voltage source and we'd pay him to see who could withstand the highest voltage. Now, we were really men!
  12. KL7AJ

    KL7AJ E-book Developer

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    Actually, you haven't violated anything. Take the example of a perfect voltage follower, or the more practical cathode or emitter follower.

    These devices are capable of extremely high (theroetically INFINITE) power gain, for precisely the reasons you stated, while still having unity (or less) voltage gain.

    On the flip side, a transformer is capable of extremely high voltage gains, but affords no power gain.


    eric
  13. PRS

    PRS Thread Starter Well-Known Member

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    Good point. I can see I wasn't thinking about it right. Thanks.

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