# The “10x rule” for impedance bridging

Quoting the Wikipedia impedance bridging article . . .

A connection is commonly said to be bridged if the load impedance is at least ten times the source impedance.

Why the magical numer 10?

To give this question some context: If designing a preamp stage for audio equipment, am I better off designing an amp stage that has exactly 10x the nominal source impedance of the connecting device (perhaps using an inverting op-amp configuration with appropriate resistances), or is it just as good (if not preferable) to use a non-inverting op-amp configuration to give a gigantic load impedance?

Why the magical numer 10?

It's an order of magnitude in the decimal system.

Nothing magical happens there; it's a matter of diminishing returns.

If your input impedance is 10 times the source, you loose about 10% of the available source voltage in the source resistance.

If your input impedance is 100 times the source, you'd loose about 1%. 10 fold increase for 9% improvement

If your input impedance is 1000 times the source, you'd loose about 0.1%. 10 fold increase for 0.9% improvement.

There's no compelling reason to design for exactly 10X the nominal source impedance.

The art of engineering includes understanding approximations and when they are "good enough" or not.

If the load impedance is at least ten times the source impedance, then most of the voltage generated by the source actually appears across the load. That is what "bridged" means: the load gets a copy of the source voltage. If the impedances are, say, equal, then half the voltage spans the source and half spans the load. So 3 decibels of voltage are lost. Ten is just a round number in the decimal system. There exist more than one such rule of thumb. For instance, for a voltage divider to be "stiff" voltage reference, its resistance should be less than 10X that of the resistance of whatever it is supplying. Or if an RC high pass filter has a corner frequency (-3dB rolloff) of f, then the "ideal" frequency response limit is considered to be at 10f, where there is little rolloff.

If you're designing an input stage for audio, you might not know the exact impedance of the previous device (if the end user can choose what device that is). So in audio there are some "ballparks" for impedance. The "line level" ballpark calls for impedances of around 10,000 ohms. A preamp stage probably does not have a line level input, but some kind of microphone, instrument pickup, or other device. In those cases, the input is tailored to that general kind of device. For a microphone you'd have an input impedance in the hundreds of ohms into somewhere past one thousand. Some microphone preamps have a variable impedance, letting users do some matching.

Too high an input impedance can be bad because it amplifies the effects of small capacitances. (Big R means big RC!) So for instance a given length of cable going into a 1 megohm input will show a worse high frequency roll-off due to cable capacitance than exactly the same cable going into a 10K input.

You can achieve a lower input impedance with a noninverting stage. Simply shunt the input to ground through a resistor and take the input from the top of that resistor.

One advantage of inverting stages is that the op-amp inputs do not track the input voltage. The + terminal is pinned to a reference voltage, and due to feedback, the - terminal stays at a very close voltage. So inverting configurations do not trigger op-amp common-mode issues, like limited common-mode input ranges, or common-mode distortion. The inverting configuration lets you configure gains less than one, and that lets you use input signals that swing beyond the power rails and it can all work out. With the noninverting stage, you can at best use a passive attenuator to trim a large input signal down to zero, since you can't do it with gain. Speaking of being able to configure a gain down to zero, with the inverting stage you can do that for high frequencies. With a noninverting stage, if you have maximum feedback at high frequencies, the best you get is unity gain. Inverting stages are also useful for mixing audio signals with little or no crosstalk between the channels. The mixing point is the - terminal, and it acts as a virtual ground across which signals from the different sources being mixed do not cross.

• "So 3 decibels of voltage are lost". A factor of 1/2 is 3dB for power but 6dB for voltage: $20 log(0.5) = -6.0 dB$ – Alfred Centauri Nov 1 '12 at 1:23