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inherently critically damped

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In Reply to: Re: Zobel's attenuation on driver posted by abc on May 03, 1999 at 05:15:51:

To take the worst case scenerio & keep things simple :
          Re          Le
   0----/\/\/\/----)()()(---0
   |                        |
   |                        |
   +----/\/\/\/------| |----+
          Rz          Cz
Rz=Re
Cz=Le/Re^2
Zz = Rz + 1/(s*Cz)
Ze = Re + s*Le
Zeff = Zz*Ze/(Zz + Ze) = Re
Resonate Loop:
Zz + Ze == 0
we = Re/Le
damp factor = 1 (critical)
thus, there is no ringing.

Follow Ups:

Re: inherently critically damped hZ 23:34:35 5/03/99 (3)
That post looked very educational, but I didn't quite understand it. Could you clarify / explain the purpose of the circuit you demostrated and it's purpose?
- Re: inherently critically damped Mart 00:35:37 5/04/99 (2)
  a driver can be accurately aproximated by:
```
  
     +---)()()()(--+ 
     |             | 
     |             |  
 0---+---/\/\/\/---+---/\/\/\/\---)()()()(---0 
     |             | 
     |             | 
     +-----| |-----+ 
  
```
  However, the left half approximates the speaker's LF near fs. Thus, we can shorten it to:
```
  
        Re        Le 
 0---/\/\/\/\---)()()()(---0  
  
```
  where "Re" & "Le" are among the common Thiel-Small parameters of the speaker:
  Le : voice-coil inductance in Henries
  Re : DC resistance
  This is the Zobel circuit:
```
  
        Rz        Cz 
 0---/\/\/\/\---| |---0  
  
```
  When the 2 are wired in parallel the effective impedence is purely resistive at the higher frequencies.
  The preceeding post was talking about a resonant reactance current between the cap & choke. The frequency {fe} is defined as:
  2*Pi*fe == 1/Sqrt[Le*Cz]
  However, in a LRC circuit the damping factor (del) is:
```
  
 +---/\/\/\/\---+ 
 |              | 
 |              | 
 |            ----- 
 | 
 |            ----- 
 |              | 
 |              | 
 +---)()()()(---+ 
  
```
  del == R*Sqrt[C/L]/2
  In our case
  R = 2*Re
  L = Le
  C = Cz = Le/Re^2
  thus
  del == 2*Re*Sqrt[Le/(Re^2*Le)]/2 == 1
  If del is less than one the circuit rings, above one the circuit is slow & makes the sound dull.
  If you need more info, it's time to grab a basic electronics book.
  - thanks hZ 14:06:58 5/04/99 (1)
    That did help. Also reminded me that the only thing mathematical I really enjoy is electronics. I will have to take that "Foundation of Electronics" book off the shelf and open her back up. Thanks!
    - do yourself a favor ... Mart 16:47:17 5/04/99 (0)
      and open that book (while thumbing through your memorized cookbook). You'll understand both much better.

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