Impedance Response – what’s that? Why do we

need it? What’s it good for? That’s what I’m going to explain today. Hi there, this is Marius Loubeeka from Hamburg,

Germany and welcome to the Loubeeka Podcast number 2! Our today’s topic is Impedance Response.

I also call it Impedance Plot. The German version is linked in the comments below. First of all the impedance plot is a Bode

plot: the x axis is scaled logarithmically as in a frequency response plot. All decades

have the same width. That means that 10 to 100 Hz is for example as wide as 100 to 1000

Hz. Basically it depicts the resistance of a speaker at every single frequency because

speakers are a complex system. They contain a system similar to a mass connected to a

spring which causes the peak at the resonant frequency. The pole piece enlarges the inductance

of the voice coil which causes the rising ramp to high frequencies. Other resonances

within the driver can also cause peaks in the plot. Even a normal resistor does not

have a linear plot because firstly if they are made from a wound wire they have a small

inductance and secondly any in wire the proximity effect increases towards higher frequencies.

At high frequencies electrons tend to move only on the surface of a conductor and therefore

the resistance, the real part of impedance, increases. That of course is also the case

on a wound wire. It can be prevented by using multistrand wires, which have a bigger surface

than solid wires of the equivalent cross sectional area. But inside a resistor you usually have

solid wires. Thus the proximity effect can be observed from about 1 kHz on. The impedance response reveals much information

about the driver and even more about a complete speaker. Mainly the region between 0 and 20,

or let’s say 25, ohms is most interesting. If you only look at that range you have a

higher resolution and are able to recognize resonances better, or whatever interesting

there is to see. It is for example easier to determine the nominal impedance of a complete

speaker which is the lowest value in the whole range of 20 Hz to 20 kHz. A German Industrial

Standard defines that the minimum may be 20% less than the nominal value i.e. e.g. 3.2

ohms for a 4 ohms speaker. If the value is less than 3.2 ohms it has to be called 3 or

2 ohms depending on how low the value exactly is. The top of the peak at the resonant frequency

may be located outside of the diagram because it is only necessary to know the exact point

and value for TSP calculation. But that’ll be another podcast. Usually it is more interesting

to have more resolution to be able to see other things more clearly. Smaller peaks in

other parts of the plot may indicate further resonances. To find out exactly you have to

look at the distortion plot and the waterfall diagram and see if there are also resonances

visible at the same frequencies. Especially if they are visible on all three plots they

might be audible. If they’re not visible on all of them you can’t be sure but you know

what to look for in a listening test. The impedance plot of a whole speaker tells

you something about the enclosure type, number of ways and the crossover network. You can

see if the crossover network contains series or parallel RLC circuits. Series RLC circuits

in parallel to the driver usually cause a dip in the plot and parallel RLC circuits

in series to the driver cause a peak. Parallel RLC circuits in series to the driver are mostly

found in fullrange speakers – another topic for a future podcast. In multi-way speakers

peaks are normally near crossover frequencies. – A closed box has one peak in the bass.

– A high pass filtered closed box has a ramp below that towards the low bass because the

capacitor in series has a high impedance at low frequencies.

– A bass reflex box has a double peak with a minimum in between at the tuning frequency

of the port. At the crossover frequencies there is usually also a high peak.

– A horn speaker has many peaks in the bass which sometimes are very close to or overlap

each other. That is due to the fact that horns amplify several frequencies and also cancellations

appear. – A transmission line cannot clearly be determined

by looking at the impedance plot. There might be only one or even two peaks, that varies

depending on the design of the line. I looked at several projects in the German DIY magazine

Hobby HiFi and their impedance responses look really different. Another reason for that

is that Hobby HiFi often uses internal Helmholtz absorbers, Helmholtz absorber chambers, to

suppress particular resonances which therefore might not appear on the impedance plot.

– A leaky closed box can also be recognized. This is basically a bass reflex box where

the port is filled with absorber material. You use this for drivers with a high Qts,

mostly>1, that do not work well in either bass reflex or closed boxes. In a closed box

their frequency response has a high peak in the bass and the well-defined leak in comparison

attenuates that peak a bit. The impedance plot looks similar to a normal closed box

with the difference that the impedance peak at the resonant frequency is asymmetrical.

The lower slope of that peak is not as steep as the higher slope. It looks more like a

sawtooth. I’m planning on making podcasts about enclosure types and then I’ll also tell

something about leaky closed boxes. You can also determine how big the output

impedance resp. the damping factor of the amplifier needs to be from looking at the

impedance response of a speaker. If the speaker has a big range in impedance the output impedance

of the amp needs to be small i.e. the damping factor has to be big. Valve amps for example

have the disadvantage of high output impedances which may be even 3, 4 or 5 ohms. That forms

a voltage divider with the speaker which causes a deformation of the frequency response of

the whole system. The more the impedance varies the more the frequency response gets deformed.

The impedance response is also probably important in combination with class-d amplifiers, aka

digital amps. Tests of those in Hobby HiFi showed that some have the same effect at high

frequencies. This is caused by the low pass filter which is installed on their speaker

terminals to filter out the carrier frequency. The cut-off frequency of this low pass is

determined by the impedance of the speakers and can cause am amplification at a high impedance

or an attenuation at a low impedance. How much depends on the inductance of the coil.

It might be up to 2 to 3 dB. Another thing you can see in impedance responses

of bass reflex boxes is the Q factor of the enclosure. In Hobby HiFi issue 4/2004 for

example you find an article about how to calculate this from measuring the height of the minimum

between the two peaks in the bass in comparison to the DC resistance. Basically this shows

how leaky the box is and especially in a bass reflex box you want the acoustical energy

to leave only through the port and not lose it through gaps or deformation of walls. Furthermore with the help of an impedance

response you can measure capacitance and inductance values of crossover parts. By measuring the

impedance curve of capacitors, coils and resistors in the software LIMP, which I use, you can

calculate resistance and capacitance or inductance by one click at any frequency where you place

the cursor on the plot. That works, because LIMP also measures the phase of the impedance.

Impedance, in equations represented by the letter Z, not only consists of the argument

of Z which is shown in the impedance response but also of the phase difference between voltage

and current. Okay, buckle up, now we take a short detour through the kingdom of complex

numbers and the complex calculation of alternating current. You can depict impedance as polar

coordinates for one frequency. The argument of Z from the impedance plot is the length

of the pointer at one particular frequency in polar coordinates and the angle between

the pointer and the positive x axis is the phase. You could also calculate Cartesian

coordinates from that. The x value is the real part of the impedance, the y value the

imaginary part. For an ideal resistor the real part is exactly the resistance and the

imaginary part should be zero. For ideal capacitors and inductors the real part is zero and the

angle is plus or minus 90 degrees. In German we have two nice mnemonics: “im Kondensator

eilt Strom vor” something like “in a capacitor the current hurries to be the first” and “in

Induktivitäten die Ströme sich verspäten” which means “in inductors the currents are

late”. I also found an English mnemonic for that: “ELI the ICE man” E stands for voltage,

I for current, L is an inductor and C a capacitor. Now ELI, E-L-I, means: E leads I in an L,

i.e. voltage leads current in an inductor, and ICE means: I leads E in a C, i.e. current

leads voltage in a capacitor. This shows the shift between voltage and current. Basically

this a bit too complicated to describe it only with words. It might be a topic for a

video. On the other hand there’s the possibility to look it up at Wikipedia. There might be

a descriptive sketch to understand it better. That’s all for today. Next planned topics

are crossover networks, distortion plot, waterfall spectrum, Thiele-Small parameters and various

enclosure types. If you have other suggestions please write a comment below. If you found

a mistake please have a look at the comments to see if I already corrected it. If I didn’t

then leave a message! Thank you for listening and I’m happy if you listen to my other podcasts

or watch some of my videos. If you like what I do please subscribe. Until next time! Bye!

zum messen der Lautsprcher kann man sehr schön SATlive nehmen von Thomas Neumann www.satlive.audio – es gibt div PDFs mit Erläuterungen und Background als auch einen youtbue kanal der div Anwendungen zeigt