My Wiki: Sharks Teeth

Sharks Teeth

Drive the circuit with a square wave signal and look at the scope.

You get the exponential waveforms for the CR circuit and RL .

When looking at the scope trace for the CO-AX signal, it also showed a CR type wave form. Why?

The waveform was on the Hi-Z input of an E1 monitor Amp fed from a 30dB monitor tap.

If you terminated the input with Zo there was not enough signal.

The "time Constant" is "CR" for capcitor resistor CR networks has an equivalent for the Rtap CO-AX circuit.

  delta T X steps in Voltage

similar to Numerical Integration

  h x gradient

Consider the Gradient of the waveforms at the start and compare the equations that have equal gradients.

The "time Constant" is

 TimeConstant = "CR" = ( length of Un terminated Co Ax) / 100 x microseconds x ( Zo + Rtap ) / Zo

 "CR" * Zo = Length/speed  * ( Zo + Rtap )

So there is no proportial equivalent but I have an understanding!

If Rtap is much greater than Zo it simplifies to

 "CR"  ~=  Length/speed  * Rtap/Zo

I did a course at college about using CO-AX to model electronics!

Now you use a digital computer.

Examples CO-AX reflecting

Drive a length of cable , 14m of RG58 and we see the steps due to reflections off an open circuit.

We see Shark Teeth waveforms on the outputs of our video amps. Is this due to CR or the CO-AX reflections?

The expected waveforms should be like:

This is what the monitor amp waveform looks like, but they work.

No Steps are seen. The Cable lengths we are not seeing steps due to reflections.

http://www.coax-connectors.com/products/connectors/type-43/43-533-d6-9b-u-link.aspx

http://www.interfacecomponents.com/connectors_TYPE-43.html

Video Amp Have Shark Tooth Waveforms - INPUT

The input of the Amp may be a length of cable fed from a 30db CO-AX tap.

https://pervisell.co.uk/telecomms/index.html

Specification:

Input:

: Inputs can be used with 0dB to -30db protected monitor points.
: (This represents an effective series resistance of 2400 ohms - This value may vary from 470 ohms to 4700 ohms with no signal degradation.)
: Maximum recommended cable length 1m - 3m depending on local conditions.
: Please note that we have occasional enquiries for 64 Kb versions; usually this refers to the demultiplexed data channels data rate.
: The actual data rate of the multiplexed stream is actually 2048 Kb.

This is a CO-AX link with a 2400 ohm resistor.

 |
 +---[ 2400 ]--- == 75 ohm CO-AX == Hi-Z input
 |

  k = 75 / ( 2400 + 75 ) = 0.0303 or 3% increase each reflection.

A CO-AX 1m long would reflect , there and back takes 10ns

So for an E1 488ns __--__ or 244 ns there would be 24 steps.

This is a CO-AX link with a 2400 ohm resistor.

 |
 +---[ 2400 ]--- == 75 ohm == Hi-Z input
 |

  k = 75 / ( 2400 + 75 ) = 0.0303 or 3% increase each reflection.

The CO-AX 1m long would reflect , there and back takes 10ns

So for an E1 488ns __--__ or 244 ns there would be 24 steps.

For a 30dB Tap with series resistor:-

Tap: -30.37db 2400.00 ohms loss 30.37db

step	Vnode/Vout
1	0.030303030303030304
2	0.05968778696051423
3	0.08818209644655926
4	0.11581294200878474
5	0.14260648922063976
6	0.16858811075940824
7	0.19378241043336558
8	0.21821324648083937
9	0.24190375416323817
10	0.2648763676734431
11	0.28715284138030844
12	0.30875427042939
13	0.3297011107194085
14	0.3500131982733658
15	0.36970976802265776
16	0.38880947202197114
17	0.4073303971122144
18	0.42529008204820795
19	0.4427055341073532
20	0.4595932451950091
21	0.475969207461827
22	0.4918489284478323
23	0.507247445767595
24	0.522179341350395
25	0.536658755248868
26	0.5506993990292053
27	0.5643145687555929
28	0.577517157581181
29	0.590319667957509
30	0.6027342234739481
31	0.6147725803383739
32	0.6264461385099382
33	0.6377659524944856
34	0.6487427418128345
35	0.6593869011518396
36	0.6697085102078445
37	0.6797173432318492
38	0.6894228782854295
39	0.698834306216174
40	0.7079605393611385
41	0.7168102199865585
42	0.7253917284718143
43	0.7337131912453957
44	0.7417824884803836
45	0.7496072615567357
46	0.7571949202974406
47	0.7645526499853968
48	0.7716874181676576
49	0.7786059812534861

It takes 33 steps to get to the 63% T=CR TimeConstant. Each Step takes the There and back time of ( length x 1/100 ) microseconds per metre.

For a 10dB Tap with series resistor:-

Tap: -9.99db 162.00 ohms loss 9.99db

step	Vnode/Vout
1	0.31645569620253167
2	0.5327671847460342
3	0.6806256705858967
4	0.7816934963498535
5	0.8507778329480011
6	0.898000037711292
7	0.930278506789997
8	0.9523422704640485
9	0.96742383044378
10	0.9777327448603053
11	0.9847793445880568
12	0.9895960076931022
13	0.9928884103218673
14	0.9951389133845674
15	0.9966772319337549
16	0.9977287408154781
17	0.9984474937219724
18	0.9989387931770445
19	0.9992746181210177

It takes 3 steps to get to the 63% T=CR TimeConstant, or 30 ns.

simulated using:-

 <script>

  var opStr = ""

  // 10 dB Tap
  var Zout = 162
  var k = 75 /( 75 + Zout ) 
  self.document.write( "|| step  ||  Vnode/Vout  || \n" )	
  var Vout=50
  var Vnode=0
  opStr += "0,"
  for( x=1 ; x < 20 ; x++){
    Vnode = ( Vout-Vnode )*k + Vnode
	opStr += Vnode +" , "
	self.document.write( "|| "+ x + " || " + Vnode/Vout + " || \n" )	
  }

  // 30 dB Tap
  var Zout = 2400
  var k = 75 /( 75 + Zout ) 
  self.document.write( "|| step  ||  Vnode/Vout  || \n" )	
  var Vout=50
  var Vnode=0

  opStr	+= "0,"
  for( x=1 ; x < 50 ; x++){
    Vnode = ( Vout-Vnode )*k + Vnode
	opStr += Vnode +" , "
	self.document.write( "|| "+ x + " || " + Vnode/Vout + " || \n" )	
  }

  //
  // Output driving 8 x -- [ 75 ohm ] --|=== 75 ohm co-ax ===
  //
  self.document.write( "|| step  ||  Vnode/Vout  || \n" )

  var Vout=50
  var Vnode=0
  var Zout = 25
  var k = (75/8)/( 75/8 + 25 ) 
  opStr	+= "0,"
  for( x=1 ; x < 50 ; x++){
    Vnode = ( Vout-Vnode )*k + Vnode
	opStr += Vnode +" , "
	self.document.write( "|| "+ x + " || " + Vnode/Vout + " || \n" )	
  }

 </script>

Simulating the Output.

step	Vnode/Vout
1	0.2727272727272727
2	0.47107438016528924
3	0.6153268219383922
4	0.7202376886824671
5	0.796536500859976
6	0.8520265460799825
7	0.8923829426036236
8	0.9217330491662717
9	0.943078581211834
10	0.9586026045176975
11	0.9698928032855981
12	0.9781038569349805
13	0.9840755323163495
14	0.988418568957345
15	0.9915771410598873
16	0.9938742844071907
17	0.9955449341143207
18	0.9967599520831424
19	0.9976436015150126
20	0.998286255647282
21	0.9987536404707505
22	0.9990935567060003
23	0.9993407685134548
24	0.9995205589188763
25	0.9996513155773645
26	0.9997464113289923
27	0.9998155718756309
28	0.9998658704550043
29	0.9999024512400031
30	0.999929055447275
31	0.9999484039616544
32	0.999962475608476
33	0.999972709533437
34	0.9999801523879541
35	0.9999855653730576
36	0.9999895020894963
37	0.9999923651559973
38	0.9999944473861798
39	0.9999959617354035
40	0.9999970630802935
41	0.9999978640583953
42	0.9999984465879238
43	0.9999988702457628
44	0.9999991783605547
45	0.9999994024440398
46	0.9999995654138472
47	0.9999996839373434
48	0.9999997701362497
49	0.9999998328263634

Video Amp Have Shark Tooth Waveforms - OUTPUT

Another type of E1 "video" monitor amp drives 8 x 75 ohm cables. The signal has a pronounced Shark tooth shape.

The output is probably designed to drive a circuit:

   Amp ---[ 75 ohm ] ---===75ohm coax === | === 75Ohm coax === | -- [75 ohm load ]--

In reality the Amps are driving 8 lengths of un terminated 75 Ohm cable

   Amp,Vout --[ Zout ] --+---=== 75ohm coax === | O/C
                         |
                         +---=== 75ohm coax === | O/C
                         |
                         +---=== 75ohm coax === | O/C
			 |
		         +- Vnode

So while the signal is traveling down the 75 ohm coax, it is 75 Ohm resistor.

When the signal bounces off the O/C and back, it is then High Z.

The 75 ohm resitor between the Amp and Co-ax absorbs the reflection. It is assumed that the Amp output is low impeadance.

In this case, We are not seeing steps, only the Sharks Teeth.

So we can itterate:

 Vnode = Vout * K

where K is [ Zout ] / (Zout + Zco-ax/8)

When the signal bounces back for the next T bounce.

 Vnode = (Vout-Vnode)*k +Vnode

The speed of signal is 200m / microsecond, but as it got there and back 100m /micro second.

 Tbounce = length /100 microseconds.

A cable 10m long Tbounce is about 100 ns

Itterate this and you will get a CR type curve.

What is the Time constant?

For a CR network the t= CR and is when V gets to about 0.63 or = ( 1 - exp( -1 ) )

So when does the way for get to 0.63 of max. It will need more iterations the smaller K, and will be proportional to t.

If we itterate for k = 0.1 you need about 8 itterattions before Vnode gets to 63%

What is a typical Zout? 75 ohm. K = 0.11

It takes about 8 itterations to get to 63 % or the "TimeConstant"

So for a 10 metre cable it takes 8 * 100ns or 800ns.

 __---___   ___---___
         ---

</div>

  var Vout=10
  var Vnode=0
  var Zout = 25
  var k = (75/8)/( 75/8 + 25 ) 
  var opStr= "0,"
  self.document.write( "\n" )
  for( x=0 ; x<20 ; x++){
    Vnode = ( Vout-Vnode )*k + Vnode
	opStr += Vnode +" , "
	self.document.write( x+ " , " + Vnode/Vout +"\n" )	
  }
  self.document.write( "\n" )

</script>

I plotted this calculation.

Still working on the formaulae.

For a resistor Capacitor

 - - [   ] - - - |   | - - 
       R           C

The Time Constant is R x C

   V = I R

   dV/dT = I C

So the Gradient of increase in voltage is 1 when CR == 1

So for the CO-AX

  the Gradient = step / delta T

where step is

    Zo / ( Zo + Rtap ) = K

The number of Steps need is 1 / K

  Steps = ( Zo + Rtap ) / Zo

And delta T is

  Length / speed

For CO-AX there and back

  deltaT = length / 100 metres per micro second

The "time Constant" is CR and equivalent

  delta T X steps

The "time Constant" is

 TimeConstant = "CR" = ( length of Un terminated Co Ax) / 100 x microseconds x ( Zo + Rtap ) / Zo

 "CR" * Zo = Length/speed  * ( Zo + Rtap )

So there is no proportial equivalent but I have an understanding!

Related Subjects

Switched capacitor filters emulate resistance using capacitors.

  R = C x T

You let current flow into a capacitor for a proportion of time

https://pervisell.co.uk/telecomms/index.html

Terminate - Measure the voltage and dispose of the information with a termination resistor.

Th�venin's theorem and its dual, Norton's theorem, are widely used to make circuit analysis simpler and to study a circuit's initial-condition and steady-state response.

Th�venin's theorem - voltage - zero impedance in series

Norton's theorem - Current - high impedance in parallel.

The generator is low impedance.

The voltage across the Generator is V if it's own and 0 if its from the far end.

Unterminated 30m ? cable :

Terminated 30m ? cable :

reflections 11m ? cable :