impedance for idiots?

[carboncomp]

Can someone link me a good tutorials on impedance, as right now Im having real trouble grasping the concept..........got the notion of a voltage divider that is effected by frequency, and sure thats not right!   

[R.G.]

Are you solid with resistors and Ohm's law? That is, a resistance is literally how many volts are needed to force an ampere of current through the part.

Resistors are frequency-neutral. They don't care whether it's DC or 20kHz, the current through them is still the voltage divided by the resistance.

For capacitors, the amount they *impede* current flow varies with frequency. Where a 1K resistor *resists* current flow by one volt per milliampere, a capcitor *impedes* current flow by Xc = 1/(2*pi*f*C). A simpler way is to think of the 2*pi as a constant "k" which is just some number and say that the impedance of a cap is
Xc = 1/(k*f*C).
What's important there is that the *impedance* of a cap goes down as frequency goes up (f gets larger, 1/f gets smaller) and also goes down as the capacitance goes up.

So, a 1K resistor is one volt per milliampere at all frequencies. At 1kHz, a "1K" capacitor is C = 1/(2*pi*f*1k) = 0.159uF. Which means that at 1kHz, a .159uF cap with one volt of AC across it lets 1ma flow, just like a 1K resistor does.  The same capacitor with 2kHz across it lets 2ma flow because at 2kHz, its impedance is now half because the frequency is double.

Are you with me so far?

[Morocotopo]

R.G., sorry to intrude, but the topic interests me, and I think I´m getting the idea, from this post and other readings I´ve made. Could we say, just to test my understanding of it, that impedance is frecuency-dependent resistance?

[fuzzy645]

Perhaps these resources might be of some assistance as well:

Zachary Vex on Impedance: http://www.diystompboxes.com/wiki/index.php?title=Zachimpedance

Interesting youtube video lesson: http://www.youtube.com/watch?v=xyMH8wKK-Ag

Here is what I personally have found confusing.  Putting audio/pedals aside for a moment, AC wall sockets in USA are 120V with a fixed frequency of 60 Hz..  In this case, the concept of impedance seems extremely simple.  Even though reactance is frequency dependent, the frequency will never really change.  OK, now back to audio/pedals - in this case the concept seems extremely confusing to me because frequency will be changing non stop, and you can hear many frequencies simultaneously.  Play a low "E" note that is one frequency, play a screaming bend at the 18th fret, that is another frequency, play some chords, we have a symphony of frequencies.  In the world of audio so much is made of this concept yet it seem to me the input & output impedance of a device can never be pinned down for this reason. 

[deadastronaut]

youtube is my friend!...

[R.G.]

R.G., sorry to intrude, but the topic interests me, and I think I´m getting the idea, from this post and other readings I´ve made. Could we say, just to test my understanding of it, that impedance is frecuency-dependent resistance?

The more discussion, the more understanding.

There are actually several concepts involved, but yes, that is the first biggie. Reactances (that is, capacitors and inductors) limit the flow of AC currents depending on the frequency.

The reason I'm being careful and not just saying "yes, they're frequency-dependent resistors" is that I'm trying to leave the discussion door open for what they do to phase. That's why I'm saying " frequency dependent limiter of AC current" instead of just "resistor". Yep, your concept is correct for an isolated capacitor.

[R.G.]

Here is what I personally have found confusing.  Putting audio/pedals aside for a moment, AC wall sockets in USA are 120V with a fixed frequency of 60 Hz..  In this case, the concept of impedance seems extremely simple.  Even though reactance is frequency dependent, the frequency will never really change.  OK, now back to audio/pedals - in this case the concept seems extremely confusing to me because frequency will be changing non stop, and you can hear many frequencies simultaneously.  Play a low "E" note that is one frequency, play a screaming bend at the 18th fret, that is another frequency, play some chords, we have a symphony of frequencies.  In the world of audio so much is made of this concept yet it seem to me the input & output impedance of a device can never be pinned down for this reason. 

There are two fundamentally different views of the world in electronics, and sooner or later if you keep doing electronics, you have to learn the two views and flip backwards and forwards between them. These are the time-domain and frequency domain views.

Time domain is what we are all used to thinking of. It's what you see on an oscilloscope - the signal voltage wiggling up and down.

Frequency domain is what we hear, but don't have a good intellectual picture of. We can easily hear a signal which has two notes/frequencies in it, and tell roughly how much of which one is there. At any instant, the signal has one signal voltage value. The frequency content has no meaning at one instant. Over some time, the signal traces out a waveform which is composed of possibly many frequencies. The signal voltage over a period of time has only averaged (in some way) values, but it has a specific set of frequencies which make it up. This is usually presented as a frequency spectrum, a graph of how big each component frequency is in the signal.

In your example, the low E is probably some amount of 82Hz, and varying amounts of 164Hz, 246Hz, 328Hz, and so on, the frequencies being 1, 2, 3, 4, ... times the base note frequencies. The screaming bent lead has the same kind of structure, a fundamental and harmonics, but the bend means that the fundamental and all the harmonics move in frequency over time.

The issue is confusing because you have to look at it from two different directions at the same time.

[CynicalMan]

On the practical side, you're right that there is no single input/output impedance for most effects. But for most effects, the impedance varies very little, and we just quote a single value for simplicity. Or the impedance varies a lot but in a range that doesn't matter. Take this buffer for example:



First let's look at the input impedance.
Since +9V acts as ground for AC, we can treat the two 1M resistors as if they're in parallel, or 500k. The input impedance of the op amp is incredibly high, so we'll ignore that. So the input impedance is the impedance of the capacitor + 500k. Now, let's look at either end of the audible range, using the formula for capacitive reactance: 1/(2*pi*C*f). At 20Hz, the capacitor's impedance is 1/(2*pi*100*10^(-9)*20), or 79kΩ. At 20kHz it's 79Ω. So, the input impedance varies from 500kΩ to 579kΩ. That's effectively 500kΩ throughout the audio spectrum, it only varies by 16%. So for that we'd usually just say a 500kΩ input impedance because it's very rare for us to have to worry about such a small change.

Now, the output impedance.
The output impedance of the TL071 is around 160Ω IIRC. So the output impedance is the 10uF capacitor's impedance + 160Ω. Again, let's look at 20Hz and at 20kHz. At 20Hz the capacitor's impedance is around 790Ω. At 20kHz it's 0.79Ω. So here there's a lot bigger a variation, but it still doesn't matter much. For our purposes, an output impedance from 160Ω to 950Ω will still drive just about any cable and audio equipment without any problem. It will not drive a speaker, but that's not what a buffer like this is made for. So the output impedance is too small to worry about throughout the audio spectrum. If you have to pick one value, calculate it at 1kHz. That's very close to the middle of the audible frequency range, and it's often used as the standard frequency for audio specs. For this circuit, the output impedance at 1kHz is around 180Ω.

Hopefully this is comprehensible, but if not, read up a bit more and come back to this. This does sort of need the frequency domain thinking that RG is talking about. With impedances, unless you're looking at phase, you should be thinking in terms of the frequency domain. I'd suggest playing around with frequency response analysis in a circuit simulator like LTSpice. That helps a lot in wrapping your head around impedance.

[DavenPaget]

@Cynicalman , then why are some buffers made with 1uF output caps ? That would be 7.9K @ 20Hz and 7.9R @20kHz ... what was the author trying to accomplish ? Because that is quite some roll-off .

[CynicalMan]

1uF works fine, and 0.1uF usually works too. I can do calculations for all this if you want, but I don't want to confuse the OP with extraneous math.

The main things that buffers are trying to drive are cable capacitance and the input impedance of the next stage. Cable capacitance usually only significantly affects the upper frequencies. And the buffer's output impedance is much lower at higher frequencies, so it can drive the capacitance just fine. With guitar gear, the input impedance of the next stage is usually pretty high, so even a output impedance that goes up to 7.9k won't hurt.

Also, with guitar gear we don't need to handle 20-20kHz. 50-10kHz will do fine and you can often get away with less.

Edit: I should mention that the 50Hz to 82Hz range is not normally used for string vibration but can be heard with percussive techniques.

[therecordingart]

The more discussion, the more understanding.

There are actually several concepts involved, but yes, that is the first biggie. Reactances (that is, capacitors and inductors) limit the flow of AC currents depending on the frequency.

The reason I'm being careful and not just saying "yes, they're frequency-dependent resistors" is that I'm trying to leave the discussion door open for what they do to phase. That's why I'm saying " frequency dependent limiter of AC current" instead of just "resistor". Yep, your concept is correct for an isolated capacitor.

Like ELI the ICE man? Voltage leading current through an inductor and current leading voltage in a cap?

[Seljer]

Depends on what you expect the input impedance of the next stage to be and how low you need the frequency to go. Your requirements may not be so strenuous. For a guitar the low E is only 82Hz. The reactance of 1uF at 82Hz is about 2000ohms. If the input impedance of the next thing is at least a couple of 10 kiloohms this value is not an issue.

Also you can get 1uF as a reasonably sized non-electrolytic capacitor with better electrical properties than its polarized electrolytic counterpart.

[DavenPaget]

1uF works fine, and 0.1uF usually works too. I can do calculations for all this if you want, but I don't want to confuse the OP with extraneous math.

The main things that buffers are trying to drive are cable capacitance and the input impedance of the next stage. Cable capacitance usually only significantly affects the upper frequencies. And the buffer's output impedance is much lower at higher frequencies, so it can drive the capacitance just fine. With guitar gear, the input impedance of the next stage is usually pretty high, so even a output impedance that goes up to 7.9k won't hurt.

Also, with guitar gear we don't need to handle 20-20kHz. 50-10kHz will do fine and you can often get away with less.

Oh yeah , i just remembered . 50Hz is the lowest and somewhere around 10kHz will the harmonics peak out .
And the next equipment in line is always like 1M impedance .

[R.G.]

like ELI the ICE man? Voltage leading current through an inductor and current leading voltage in a cap?

Yes, but let's not dive all the way in until the OP understands the concept of reactances "impeding" the flow of AC current.

[Morocotopo]

This is getting interesting. Great explanations people! It´s funny how just reading once or twice about a subject is not enough to fully grasp it, you need to discuss/experiment/practice to really "get it".
R.G., hmmm, what about phase? C´mon! C´mon!
Just joking. Let´s wait for the OP of course.

[PRR]

"Impedance" is the general concept.

One specific concept is "Resistance". This is an impedance V/I which is constant for ALL frequencies, voltages, currents, etc of interest. Simple because it is constant. Useful because with carbon or iron we can make practical resistors which are very nearly constant for nearly all uses.

The next least-simple concept is "Reactance". This is an impedance which varies with frequency. Capacitive impedance gets less as frequency goes up. Inductive impedance gets higher as frequency goes up.

But there are other impedances. The impedance of a diode (or transistor or tube) varies with current and voltage. A Si diode is 30 ohms at 1mA and 3 ohms at 10mA, following this law pretty good from 0.000,1mA to 100mA. An electric motor's impedance changes with speed and/or load. A loudspeaker's impedance varies with frequency but not in a "simple reactance" way (it takes several resistors and reactances to approximate a loudspeaker's main impedance features).

There is also a distinction between small-signal and large-signal impedance. As shown below, a TL072's output impedance is much lower than a loudspeaker, IF the signal is very small. It clips at 20mA, or 0.16 volts in 8 ohms. For any larger signal its output impedance is 500-1,000 ohms, meaning it won't drive less than 2K loads well.

Ideally we would say resistance or reactance when we deal with simple resistances or reactances. However many practical cases are not-so-simple. Anyway a lot of writers get hung-up on the word "Impedance" and use it in every situation.


> the input & output impedance of a device can never be pinned down

In many cases we pin-down close-enough. Look at Alex's circuit. He showed the input impedance is 579k in low bass to 500k at high treble. That's constant-enough for sources typically under 100K.

We do have other cases where input impedance varies a lot. Often this is done on-purpose to introduce more response-shaping without more complexity. (This does require assumptions about the source impedance.)

> 7.9K @ 20Hz and 7.9R @20kHz ...that is quite some roll-off

Compared to typical 100K+ loads, it is hardly-any difference. 100K/(8K+100K) is 92%, 100K/(8+100K) is 99%.... you don't hear 10% changes in amplitude.

> The output impedance of the TL071 is around 160 IIRC

The butt-naked output of TL072 is hundreds of ohms, yes. But in a NFB amplifier connection this is reduced by the excess gain lost to NFB. At low guitar frequency the TL072's gain is 100,000 roughly. Your circuit is unity-gain, so the output is say 160/100,000 or 0.002 ohms. At high guitar harmonic the TL072's gain has fallen to roughly 1,000. 160/1,000= 0.2 ohms. The small-signal output impedance of all the opamps under NFB at most reasonable gains over the audio band may be penciled as "well under 10 ohms". Since all useful loads are much-much greater than 10 ohms, this may be ignored for nearly all practical purposes.

As you go on to say, the capacitor's impedance is generally >>10 ohms and dominates the box's output impedance. This matters to the load, but since guitar-chain loads are typically >7.9K we may mostly pretend the cap's impedance is negligible. (And often a lead guitar sound wants to lose some bass heaviness, so an "undersized" cap may be desirable.)

rg> Are you solid with resistors and Ohm's law?

This is the BIG point. Most students need more work with very simple resistor-battery problems. Most audio "impedance problems" may be handled as "resistance problems" and get answers close-enough to know how it will work.

For example: I give you a 1V battery, a 7.9K resistor, and a 100K resistor in series. What is the voltage across the 100K? Now I change the 7.9K to 7.9 ohms, what is the voltage across the 100K? Are they same, different, or really similar? Try again but with 790K.

[fuzzy645]

On the practical side, you're right that there is no single input/output impedance for most effects. But for most effects, the impedance varies very little, and we just quote a single value for simplicity. Or the impedance varies a lot but in a range that doesn't matter. Take this buffer for example:



First let's look at the input impedance.
Since +9V acts as ground for AC, we can treat the two 1M resistors as if they're in parallel, or 500k. The input impedance of the op amp is incredibly high, so we'll ignore that. So the input impedance is the impedance of the capacitor + 500k. Now, let's look at either end of the audible range, using the formula for capacitive reactance: 1/(2*pi*C*f). At 20Hz, the capacitor's impedance is 1/(2*pi*100*10^(-9)*20), or 79kΩ. At 20kHz it's 79Ω. So, the input impedance varies from 500kΩ to 579kΩ. That's effectively 500kΩ throughout the audio spectrum, it only varies by 16%. So for that we'd usually just say a 500kΩ input impedance because it's very rare for us to have to worry about such a small change.

Now, the output impedance.
The output impedance of the TL071 is around 160Ω IIRC. So the output impedance is the 10uF capacitor's impedance + 160Ω. Again, let's look at 20Hz and at 20kHz. At 20Hz the capacitor's impedance is around 790Ω. At 20kHz it's 0.79Ω. So here there's a lot bigger a variation, but it still doesn't matter much. For our purposes, an output impedance from 160Ω to 950Ω will still drive just about any cable and audio equipment without any problem. It will not drive a speaker, but that's not what a buffer like this is made for. So the output impedance is too small to worry about throughout the audio spectrum. If you have to pick one value, calculate it at 1kHz. That's very close to the middle of the audible frequency range, and it's often used as the standard frequency for audio specs. For this circuit, the output impedance at 1kHz is around 180Ω.

Hopefully this is comprehensible, but if not, read up a bit more and come back to this. This does sort of need the frequency domain thinking that RG is talking about. With impedances, unless you're looking at phase, you should be thinking in terms of the frequency domain. I'd suggest playing around with frequency response analysis in a circuit simulator like LTSpice. That helps a lot in wrapping your head around impedance.

Yes, that was very comprehensible. Thank you.   It is interesting when you actually do the math at each end of the spectrum.

Now, on the input impedance, if we change your circuit to use a .01 uf instead of a .1 uf, we have a much more dramatic swing of capacitive reactance ranging from 795K at 20 Hz vs. 795 ohms at 20 kHz.   In fact, I have noticed doing the math that a very small value capacitor will result in a HUGE swing in the capacitive reactance ranging from 20 Hz to 20 kHz, but the larger the cap will result in  much less of a differential.  For example, if we now use a 1000 pf capacitor the reactance of the cap ranges from  7.9M at 2 Hz down to a  7.95 K at 20 kHz.  

Granted, in this particular circuit the swing large or small of the cap might not make much of a difference, but in other circuits it might.

There are two fundamentally different views of the world in electronics, and sooner or later if you keep doing electronics, you have to learn the two views and flip backwards and forwards between them. These are the time-domain and frequency domain views.

Thanks RG - that is helpful.  I will first read up a bit on this concept and I'm quite sure I'll be back with questions

[DavenPaget]

1000pf is 10nF so it's NOT 7.95R but 7.95k .

[fuzzy645]

1000pf is 10nF so it's NOT 7.95R but 7.95k .

1000 pf = 1 nanofard = .001 microfard = 0.000000001

I checked my math (in Excel) and you are correct.

Here is the math at 20 hz

PI   3.141592654
UF   0.001
Converted to Farads   0.000000001
Hz   20
Z   7,957,747 (or 7.9 M)

Here is the math at 20 KHZ
PI   3.141592654
UF   0.001
Farad Conv.   0.000000001
Hz   20000
Z   7957.747155 (or 7.9K)

[DavenPaget]

1000pf is 10nF so it's NOT 7.95R but 7.95k .

1000 pf = 1 nanofard = .001 microfard = 0.000000001

I checked my math (in Excel) and you are correct.

Here is the math at 20 hz

PI   3.141592654
UF   0.001
Converted to Farads   0.000000001
Hz   20
Z   7,957,747 (or 7.9 M)

Here is the math at 20 KHZ
PI   3.141592654
UF   0.001
Farad Conv.   0.000000001
Hz   20000
Z   7957.747155 (or 7.9K)

OOPS . Calculation error .