Impedance 101: Part Two

Research for this two-part series reinforced the value of experience. My math skills might have been better in college, but impedance is one of those
Publish date:
Social count:
Research for this two-part series reinforced the value of experience. My math skills might have been better in college, but impedance is one of those

Research for this two-part series reinforced the value ofexperience. My math skills might have been better in college, butimpedance is one of those multidimensional “concepts”that I organically understand and better appreciate nowvs. then. Using carefully chosen analogies along withthree interface examples, I hope to demonstrate the common,everyday effects of impedance.

The term “interface” is equally important, becauseit implies the interconnection of two devices — a source anda destination — each having defined impedance. Like the timebefore the well-tempered clavier — when transposing a songfrom one key to another was not an option — thereare interface combinations that beg for a “professionaltuner.”

As you may recall from the last installment, I pointed out thatwire is not a perfect conductor — it has resistance —and two wires translate into a complex assortment of seriesresistance and inductance, combined with parallel capacitance. Thelong and short of interfacing is simply this: Well-designedequipment can tolerate wiring variations, while other gear live anddie by cable performance. Understanding what's good, bad andpotentially ugly will help to maximize performance and minimizedestruction to your wallet and your sound.


A loudspeaker is like a drumhead, tuned real low by a softedge-suspension material made of rubber, foam or paper. The partyou can't see is a coil of wire centered in a strongly focusedmagnetic field. Talk about complex impedance, here you have amechanical resonator mounted to a resonant chamber (a cabinet)coupled with the voice coil, the inductor known as “L”in electrical circles. A loudspeaker is technically a“motor,” but it can also be used to generateelectricity just as a dynamic microphone does. As anelectromechanical device, it is the perfect example for makingimpedance tangible.

Loudspeakers come in various sizes and shapes for theirrespective purposes. The published AC impedance willtypically be 4, 8 or 16 ohms, often referred to as“nominal,” because the magnitude changes withfrequency and is therefore averaged. The DC resistancewill be a different number. As you can see in Fig. 1, bothimpedance (the blue arrow) and phase (the red arrow) meander acrossthe frequency spectrum for a passive, two-way monitorsystem. Note that the combined woofer and cabinet resonance raisesthe impedance to a whopping 25 ohms at about 45 Hz!


To test for woofer resonance, simply insert a 100-ohm resistorin series — between it and the amp — and slowly sweep asine wave oscillator from lowest frequency to the midband. Youwon't need any other test equipment other than ears and eyes tofind the resonant “bump.”

The next impedance demonstration also requires a speaker and anamp, but sans resistor. Assuming the power amp isconnected and turned on, tap on the woofer and listen closely tothe resonance. Now, disconnect one of the amp wires (or turn theamp off) while tapping and notice the difference. (Allow enoughtime for the amp to be fully “off.”) The transitionfrom a tight, well-damped “tap” on paper to aless-restricted tonal “thud” should be obvious.

The woofer has a natural free-air resonance that changes onceinstalled into a cabinet, either ported (bass reflex) or relativelyairtight (air suspension). The speaker's nominalelectromechanical impedance is at least a factor of 10 higher thanthat of the amplifier's source impedance. The ratio of thetwo is called the Damping Factor (DF), which is responsible forkeeping the bump in Fig. 1 under control, unless the cableresistance becomes a contributing factor.

Note: While a power amp's output stage is relatively simple, itcan be further reduced to a single component for the purpose ofdefining its impedance — how the outside world sees it— the result of this reduction process, known as the TheveninEquivalent, is typically below 1 ohm. Do not confuse this with therecommended “load” or destination impedance found onthe back panel of most amplifiers.


Tapping the woofer with a finger is just the reverse of itreproducing a kick drum; both are impulses that stimulate thewoofer and cabinet resonance. Accuracy of reproduction is notalways what sounds best to the ear; an under-damped loudspeakerwill be the dreaded sonic descriptor, “warmer.” Thebest way to tame the speaker's self-expression is by minimizing thecabling between it and the power amp, hence the concept ofself-powered monitors (or the use of “monstrously”thick cable).

A car outfitted with a spring-only suspension system wouldbounce all over the road, a spring being a high-impedance devicecompared to a shock absorber. The amplifier's extremely low-sourceimpedance appears as a “short circuit” to the woofer'snatural mechanical resonance. You could describe both the shock andthe amp as “low impedance devices that provide damping andstabilization to what would otherwise be a bouncy ride.”

Note: The need for damping is the reason a 600-ohm terminatingresistor should be connected to the output of transformer-basedgear, such as the venerable UREI LA-3 limiter, when interfaced withmodern gear. A transformer consists of two coils of wire, theelectronic equivalent of excitable springs.


That impedance varies with frequency should be more tangiblenow, what about phase? The magenta square in Fig. 1 shows how acrossover network — consisting of inductors, capacitors andresistors — affects both impedance and phase response, but tomake it more tangible…

Connect a battery to a woofer and watch how it moves in or outdepending on polarity, staying there until the power is removed.Oversimplified, phase is the minute delay of the cone as itattempts to travel to its destination. Once there, the speaker hasa strong desire to return from such an exaggerated excursion,acting as a generator when it does. This example should also helpto visualize what simple expressions such as “E-L-I the I-C-EMan” did for engineering students. Don't laugh! Type“ELI the ICE Man” into a search engine, and you'll besurprised as I was. The best link,,yielded a fabulous collection of electronic formulae, rules ofthumb and mnemonics.

E-L-I reminds us that Voltage-Leads-Current by 90°(the Phase angle) in an inductor, a coil of wire designated as“L,” “E” stands for voltage and“I” for current. I-C-E reminds us that the reverse istrue for capacitors, where Current-Leads-Voltage by90°, where “C” stands for capacitor. E-L-I theI-C-E is deep, man, but memorable for the purpose of“concept retention.”


Analog audio — in both the mechanical and electronicdomains — is slow and easy to understand. The sound ofconnecting a battery or an amplified kick drum to a loudspeakeremphasizes the keywords impulse, reaction/response timeand resonance — all of which can happen at any orall frequencies, from radio and video all the way to light.Impedance is an equal-opportunity vector, equally popular in thedata communications realm. Surely, you've encountered an SCSIterminator?

Walk into Radio Shack for antenna wire, and a knowledgeablesalesperson should ask, “300-ohm or 75-ohm?” In thiscase, the assumed frequency spectrum includes FM radio andbroadcast television (88 MHz and beyond). Digital audio's S/PDIFinterface is equivalent in bandwidth and impedance to line-levelanalog video (6 MHz and 75 ohms, respectively).

To further study the effects of impedance requires math.Plotting a graph of impedance and phase requires several formulaeplus multiple calculations at as many frequencies as possible(enough to represent the audible spectrum, for example).Fortunately, I found the perfect application(“Micro-Cap” from, which was available as ademo as a free download. I'd still be ciphering if it weren't forthis handy bit of technology, so I'll spare you the math entirelythis time around.


One day, long ago, I walked into a control room to align aTascam Model 38 analog 8-track. While playing the high-frequencysection of the alignment tape, I noticed that the machine's VUmeters did not agree with the voltmeter connected at the patchbay.Eventually, I determined that the cable capacitance was loadingdown the machine at high frequencies.

Figure 2 shows the effect of cable capacitance on the frequencyresponse of vulnerable equipment. The “inset,” aschematic of the 38's output circuit, includes a very guilty1-kilohm resistor (R117) following the op amp. The purpose of thisresistor is to protect the output amplifier from accidental shortcircuits, as well as to provide a “bias trap,” a filternetwork designed to stop high-frequency bias leakage that couldpotentially damage tweeters. (Bias is well beyond hearing range,but a little leakage could potentially become a stealth tweetereater.)

I didn't carry a capacitance meter on service calls, but thisparticular customer chose the cheapest possible cable solution,sending me on a minor detour. Back in the lab, several cable testsyielded a typical range of 50 pico-Farads per foot (pF/ft) to a lowof 20 pF/ft, this being for foil-shielded audio cable andwire-shielded computer video cable, respectively. These areacceptable values.


I fed the Tascam 38 output circuit values into Micro-Cap, theessence of which is a simple RC (resistor-capacitor) circuitconsisting of R117, a 1-kilohm resistor feeding the interconnectingcable as represented by a capacitor to ground (not shown). Thestarting value of capacitance was based on 100 pF/ft for 10 feet ofcable, incremented in 10-foot steps ending at 100 feet of cable.The resulting capacitance ranged from 1,000 pF to 10,000 pF (or0.01μF), respectively. (The actual circuit includes L102 and apair of 470pF caps to “trap” the bias signal.)

A simple RC circuit is a first-order lowpass filter (at audiofrequencies) with a slope of 6 dB per octave. (A second-orderfilter has a slope of 12 dB/octave.) An abnormally high capacitancewas chosen to simulate what happens when bad cable alone isinterfaced with a vulnerable piece of equipment. Note the“box” indicating 10 kHz being 2.5 dB down, theapproximate amount noticed during the house call.

I am not suggesting esoteric audiophile cable, only that theresults from the “lab test” should serve as your guidewhen cable shopping; contact the cable manufacturer for suchminutiae as cable capacitance. Also, most modern equipment is notsensitive to cable loading, as was the old Model 38. The solutionwould have been to add one more op amp per channel to isolate thebias trap from the outside world. Collect schematics for your gearand compare output amplifier circuits with your friends. Who knows,it could be like Pokémon for adult geeks.


When I started in this business, interfacing hi-fi to pro was adeadly combination. Then, consumer equipment was“hi-Z,” slang for high impedance, while console inputand output impedance was lo-Z, 600 ohms. Now, theinterface impedance between consumer and pro gear is morecompatible. Operating levels are the primary difference, consumergear being standardized at -10 dBv, while pro operates 11.78 dBhigher at +4 dBm (for vintage 600-ohm gear) or +4 dBu (for moderngear). Then, the impedance mismatch dropped the levelfurther and created a highpass (bass roll-off) filter in theprocess.

Note: The “V” and the “M” designated tworeferences, 1-volt RMS and 1 milliWatt (mW), respectively.

Figure 3 depicts the insert points from a Trident Series 65console. The “source” could be either the mic preamp orline input amp, pre- or post-equalizer, all determined by switches.In each case, the output op amp feeds a 100-micro-Farad (μF)capacitor and a 100-ohm resistor, much better choices for theapplication. (The Tascam circuit example was focused on R117 beingtoo large to tolerate excessive cable capacitance. Note that theseries capacitor in that circuit, C106, is 2.2μF.)

Micro-Cap's simulation successfully shows what happens in aworst case scenario, the effect of excessive resistive loading ofthe 100μF output capacitor, creating a highpass (bassroll-off) filter. The very same filtering effect might occur if theoutput capacitor deteriorated, a very common ailment that plaguesolder equipment and discussed in last year's column on“Upgrades and Maintenance Issues.”

The “load” ranged from an unlikely 100 ohms to themore typical 10.1 kilohms. Ignoring the 100-ohm load results for amoment, the Table details the frequencies that fall at the“-3dB” (half-power) point for each of the other loadvalues.

Note: The internal 100-ohm resistor combined with the external100-ohm load creates a 50% voltage divider, dropping the level 6 dBas indicated by the double arrow in Fig. 3.


In Fig. 3, the lower graph depicts the simultaneous phasechanges as the frequency is swept. Phase is one of the lesstangible effects of filtering and equalization. Modern digitalfilters can be made sans phase shift. I have not had theopportunity to make a side-by-side comparison.

Though it has not been stated directly until now, you shouldwalk away from this article knowing that a low-sourceimpedance and a high-destination impedance are normal fortransformerless gear. Even transformerless mic preamps have a5-kilohm to 10-kilohm input impedance, some are variable.(Microphone impedance is typically 200 ohms.) Meanwhile, wheninterfacing transformer-based vintage (or retro) gear with moderntechnology, remember that the output transformer should beterminated, preferably at the destination. Speaking of which, at2,500 words, I am outta here!

Eddie continues to thank Dave Hill (at Crane Song), MichaelShields, Shep Siegel and Dan Kennedy (at Great River Electronics)for their geek help and support. By the time you read this, EC willbe a dad for the second time. Visittangible-technology.comfor baby pics and tohave a virtual cigar.