zobel network proper values for clean audio

Thread Starter

mike_canada

Joined Feb 21, 2020
149
speaker.png

I can't believe I haven't found anyone explaining this anywhere on the internet.
Anyways, I want to take the output of any amplifier signal and convert it to sound through an 8 ohm speaker (lets say I bought at a flea market a long time ago with no specs) so that I can only hear sounds between about 61Hz and 20Khz (normal audio range).

The closest setup I've seen to this circuit are circuits involving the LM386 amplifier but they never explain how the component values are achieved.

Other resources state the horizontal capacitor and the speaker make up a high-pass filter and the capacitor and resistor in series make up a low-pass filter.

Can someone clarify this? and can someone tell me if the values shown are accurate?
 

Ian0

Joined Aug 7, 2020
5,814

Ian0

Joined Aug 7, 2020
5,814
Other resources state the horizontal capacitor and the speaker make up a high-pass filter and the capacitor and resistor in series make up a low-pass filter.
The first statement is perfectly correct - the capacitor removes the DC offset that happens with a single-supply power amplifier.
The second statement is completely wrong. The capacitor and resistor for another high-pass filter with the resistor as the load.
The cutoff frequency is in the 100kHz region, so the amplifier sees a 10Ω resistive load a high frequencies.
Without the Zobel, the amplifier sees the increasing impedance of the speaker inductance at high frequencies. The voltage gain is Gm x Rload so the gain starts to go up at high frequencies, just when you want it to come down to make sure that it is less than unity when the phase shift reaches 180°.
 

Papabravo

Joined Feb 24, 2006
18,964
I don't think R1 & C1 are doing much of anything for you, and the corner frequency appears to be about 42 Hz. That is where the magnitude response is 3 dB down and the phase is 45°. It doesn't do anything for high frequency noise. IMHO it is about as useful as a screen door in a submarine. The rolloff is -20 dB/decade so it is definitely a 1st order network. Sorry you've been misled.
1659907320595.png
 

Ian0

Joined Aug 7, 2020
5,814
I don't think R1 & C1 are doing much of anything for you, and the corner frequency appears to be about 42 Hz. That is where the magnitude response is 3 dB down and the phase is 45°. It doesn't do anything for high frequency noise. IMHO it is about as useful as a screen door in a submarine. The rolloff is -20 dB/decade so it is definitely a 1st order network. Sorry you've been misled.
View attachment 273387
You forgot ≈1mH in series with R2 to make a loudspeaker. A purely resistive loudspeaker cannot make any noise!
 

nsaspook

Joined Aug 27, 2009
10,094

Papabravo

Joined Feb 24, 2006
18,964
Is there a better way to do this using minimal parts? I mean without R1 and C1, I feel all I have is a high-pass filter and that means the audio could include radio frequencies (and I don't want RF mixed with the music).
I have no idea what they are trying to accomplish or why they would do that. If we know more about the overall design and had some context their intentions might be more transparent. An actual bandpass filter would certainly require additional components. Steeper skirts on the response would require a higher order filter, which would require more stages with would require more components. All that said there is a reason why you don't see high order filters.
 

crutschow

Joined Mar 14, 2008
30,419
A purely resistive loudspeaker cannot make any noise!
Au contraire.
The speaker inductance doesn't dissipate any energy so it can't contribute to the sound energy.
The inductance is an artifact of magnetic speakers, otherwise how could piezo speakers work, since they have no appreciable inductance?
The part of the impedance that converts the electrical energy to sound energy looks resistive, as does any electrical load that dissipates energy.
An ideal speaker would look only resistive, similar to an ideal transformer with a resistive load (and a speaker is a type of transformer).
 

crutschow

Joined Mar 14, 2008
30,419
It's the impedance the amplifier sees that's of interest here, so below a plot of the impedance (Vsig/Iv1) of an 8 ohm speaker with a nominal 1mH inductance along with the Zobel network:
The impedance is shown for a 3 values of the Zobel resistance.
The 1 megaohm value (yellow trace) shows mainly the increase in impedance from the speaker inductance.
The red trace shows the impedance for R1 = 100Ω.
The blue trace shows the impedance for R1 = 10Ω.

Interestingly, the 10Ω resistance shows a large peak, apparently due to parallel resonance between the speaker inductance and the Zobel capacitor.

I used 100nF for C1 since 47nF gave an even higher peak.

These results indicated that the Zobel network may not reduce the high frequency impedance as much as desired.

1659925615216.png
 
Last edited:

nsaspook

Joined Aug 27, 2009
10,094
Au contraire.
The speaker inductance doesn't dissipate any energy so it can't contribute to the sound energy.
The inductance is an artifact of magnetic speakers, otherwise how could piezo speakers work, since they have no appreciable inductance?
The part of the impedance that converts the electrical energy to sound energy looks resistive, as does any electrical load that dissipates energy.
An ideal speaker would look only resistive, similar to an ideal transformer with a resistive load (and a speaker is a type of transformer).
Sure, it's a transducer that converts electrical energy into acoustic energy. It doesn't do that by making things hot, it does that by using EM field energy that can be primary magnetic (coil speaker) or electric ( piezo speakers). The reactance is not an artifact, for a coil speaker, the speaker inductance is the energy conduit for sound energy that must be there and obeys circuit theory rules like a motor shaft provides physical force. It looks resistive (just like a antenna radiating looks resistive) because the energy moves away from the source.
 

crutschow

Joined Mar 14, 2008
30,419
it does that by using EM field energy that can be primary magnetic (coil speaker) or electric ( piezo speakers). The reactance is not an artifact
It's an artifact in the same way that the inductance of a transformer is an artifact.
An EM field that is transferring energy does not create or have inductance.
Any inductance is due to leakage or magnetizing inductance of the less than ideal transformer or speaker.
An ideal transformer or antenna presents no inductance to the load as seen by the source.
the speaker inductance is the energy conduit for sound energy
If that were true then there should be a mathematical relation between the value of inductance and the amount of energy transferred, but I'm not aware of any.
The magnetic field carries the energy, not the inductance.
I know of no requirement for inductance to be present for the transfer of EM energy.
 

nsaspook

Joined Aug 27, 2009
10,094
It's an artifact in the same way that the inductance of a transformer is an artifact.
An EM field that is transferring energy does not create or have inductance.
Any inductance is due to leakage or magnetizing inductance of the less than ideal transformer or speaker.
An ideal transformer or antenna presents no inductance to the load as seen by the source.
If that were true then there should be a mathematical relation between the value of inductance and the amount of energy transferred, but I'm not aware of any.
The magnetic field carries the energy, not the inductance.
I know of no requirement for inductance to be present for the transfer of EM energy.
You ideas are based in the simplified arena of circuit theory. Inductance/permeability is never an artifact, it's a necessary requirement for EM energy movement.
https://en.wikipedia.org/wiki/Impedance_of_free_space

Free space permittivity has a unit of F/m while free space permeability has a unit of H/m.


The permeability of a vacuum (also known as free space) is equal to approximately 1.257 x 10 -6 H/m, or 1.257 microhenrys per meter (1.257 µH/m).
 

Ian0

Joined Aug 7, 2020
5,814
Au contraire.
The speaker inductance doesn't dissipate any energy so it can't contribute to the sound energy.
The inductance is an artifact of magnetic speakers, otherwise how could piezo speakers work, since they have no appreciable inductance?
The part of the impedance that converts the electrical energy to sound energy looks resistive, as does any electrical load that dissipates energy.
An ideal speaker would look only resistive, similar to an ideal transformer with a resistive load (and a speaker is a type of transformer).
The ideal loudspeaker models as a transformer. It's inductance and resistance are Lm and Rm of the transformer primary.
The load on the secondary is the air. The air is being compressed (especially the air in the box) - that is a reactive load. The sound is the resistive part of the load (as it actually dissipates power in friction).
Real loudspeakers are 0.1% to 1% efficient - the air load can almost be excluded from the model.
Piezo loudspeakers would also make no noise if they were perfectly resistive, because a real piezo element is capacitive.
 

Ian0

Joined Aug 7, 2020
5,814
It's the impedance the amplifier sees that's of interest here, so below a plot of the impedance (Vsig/Iv1) of an 8 ohm speaker with a nominal 1mH inductance along with the Zobel network:
The impedance is shown for a 3 values of the Zobel resistance.
The 1 megaohm value (yellow trace) shows mainly the increase in impedance from the speaker inductance.
The red trace shows the impedance for R1 = 100Ω.
The blue trace shows the impedance for R1 = 10Ω.

Interestingly, the 10Ω resistance shows a large peak, apparently due to parallel resonance between the speaker inductance and the Zobel capacitor.

I used 100nF for C1 since 47nF gave an even higher peak.

These results indicated that the Zobel network may not reduce the high frequency impedance as much as desired.

View attachment 273396
The amplifier doesn't have much trouble dealing with impedance peaks in its operating frequency range - there will be others such as the two caused by bass resonance of a ported enclosure, and possibly some more from crossovers. Provided that there isn't a 6dB/octave upward slope in response at high frequencies the feedback loop can be closed with enough phase margin to keep it stable.
Leave out the zobel at your peril - it creates an amplifier that is randomly stable. Piezo tweeters will keep it stable, long speaker leads will affect the stability depending on their bulk inductance and bulk capacitance, short "audiophile" ultra-thick ultra-low-capacitance leads will tend to make it oscillate.
 

crutschow

Joined Mar 14, 2008
30,419
You ideas are based in the simplified arena of circuit theory. Inductance/permeability is never an artifact, it's a necessary requirement for EM energy movement.
And where are the equations that show that inductance is required to transfer EM energy?
Waving statements about the permittivity and permeability of free space doesn't prove you need inductance to transfer energy in a magnetic field.
An ideal antenna has no inductance, only radiation resistance.
How does it do that?
 
Last edited:

crutschow

Joined Mar 14, 2008
30,419
Real loudspeakers are 0.1% to 1% efficient - the air load can almost be excluded from the model.
But that is the resistance part of the loudspeaker load that converts electrical energy into sound energy.
Real loudspeakers do have inductance, but that's an artifact of the design..
It's not needed in theory to convert electrical energy into sound energy.
Piezo loudspeakers would also make no noise if they were perfectly resistive, because a real piezo element is capacitive.
Again, that's an artifact of the element.

Inductance and capacitance are not transducer requirements, they are artifacts of the non-ideal transducers used to convert electrical energy into sound energy.
 

Ian0

Joined Aug 7, 2020
5,814
Even an ideal loudspeaker will appear as an inductive load, because of the compliance of the air in its enclosure, and, to some extent, the compliance of the air in the room.
However, the mass if air moved looks like a capacitor, which would take care of the rising impedance.
Conclusion: An amplifier driving an ideal loudspeaker doesn't need a zobel network. For all non-ideal loudspeakers, make sure you include one.
 
Top