Working out Loundess Ratings

Now we have an end to end connection using voltages, use the phone sensitivities and these formulae to calculate the Loudness ratings, for different line lengths.

The formulae are published in "ISBN 0 86341 080 4, Local Telecommunications 2, IEE , page 29, in chapter 2 Voice communications requirements." and "p267 British Telecommunications Engineering. Vol 5 Jan 1987", as well at the PABX requirement spec BTR1050.

The Loudness Rating formulae

The PABX spec had these formulae. See the ITU P. series documents as well.

	SLR = (-1/0.0175) * log10( sumFor14freqs( 10^(0.0175 ( SMJ-WS ) ) )
	RLR = (-1/0.0175) * log10( sumFor14freqs( 10^(0.0175 ( SJe-LE-WR ) ) )
	OLR = (-1/0.0175) * log10( sumFor14freqs( 10^(0.0175 ( -LMe-LE-WO ) ) )
	STMR= (-1/0.0225) * log10( sumFor14freqs( 10^(0.0225 ( -LMeST-LE-WM ) ) )

Where:-

	SMJ is the sending electroacoustic sensitivity of the telephone circuit
	SMJ = 20 log10( Voltage across the 600 ohm Termination / Sound pressure at the Mouth Reference point ) dB rel 1V/Pa

	SJe is the receiving  electroacoustic sensitivity of the telephone circuit, where the 600 Ohm termination is replaced by a 600 ohm oscillator of EMF E volts.
	SJe = 20 log10( Sound pressure level in the artificial Ear / ( E /2 )   ) dB rel Pa / V

	LMe is the overall electro acoustic loss of the telephone circuit. It includes Exchange Line, Stone bridge and 600 Ohm termination with an extension telephone and line.
        (GEN)- [ 600 Ohm ] - [ stone bridge ] - [ line ] - [ PABX ] - [ line ] - [ Phone ]
	LMe = 20 log10( Sound pressure at the Mouth Reference point  / Sound pressure level in the artificial Ear  ) dB 

	LMeST is the electro acoustic loss of the sidetone path 
	LMeST = 20 log10( Sound pressure at the Mouth Reference point  / Sound pressure level in the artificial Ear  ) dB 
	The lowercase 'e' in SJe, LMe, and LMeST denotes values using an artificial ear.
	A stone bridge isolates the DC , and used 2uF capacitors and relays to feed current via (1.5H +200 Ohm) from the battery.
	
	So the sensitivities are stated relative to places that are simple to measure, like the plug or terminal strip or junction.

The PABX requirment document, BTR1050, had tables of Phone Sensitivites. ZC and ZB were tabulated values.

COMPLEX PHONE32 uses:

Zc = --[370]--[620R||310nf]---

and Zb, ==Zb or Zso = --[270]--[1500R||180nf]---

AnnexA which had tables of sensitivies for " BT700 TYPE TELEPHONE DATA - The following send and receive sensitivites are between MATCHED impedances. Additionally, the receive sensitivity contains an allowance for real ear loss."

Also, it had AnnexB which had tables of sensitivies for " COMPLEX IMPEDANCE TELEPHONE DATA - The following send and receive sensitivites are between MATCHED impedances. "

So the sensitivities are stated relative to places that are simple to measure, like the plug or terminal strip or junction. 

COMPLEX PHONE32 uses 
Make Zc of the exchange and Terminal, the Terminal Impedance below:-

--[370R]--+--[620R]--+--
          |          |
          +----||----+
              310nF

See Fig6 - Line impedance for minimum sidetone (Zso), p267 British Telecommunications Engineering. Vol 5 Jan 1987

--[270R]--+--[1500R]--+--
          |          |
          +----||----+
              180nF

Dougnap - 2-wire Phone / PABX / phone ITU P.79 Loudness rating calculator

Edit the source code to enter the phone and exchange data.
NOTE:OLDxx phones include le, which I remove when loading.
NOTE:COMPLEXxx phones do not include le
A.PAS did not acknowledge this, and LR's would be incorrect for COMPLEX phones.
This page models:
 [ phone ]--+--[ 2km line ]---[ Exchange ]
           NTP
    [ Zc ]--+--[ 2km line ]---[ Zc ]

The NTP is the network termination point.

[terminal]---+---[ line ]---[exchange]
            NTP
			
What is the Zc of the Terminal?
What is the Zc of the Exchange?
What is the Z looking into the line towards the Exchange at the NTP?
What is the Z looking into the line towards the Terminal at the Exchange?

Make Zc of the exchange and Terminal, the Terminal Impedance below:-

--[370R]--+--[620R]--+--
          |          |
          +----||----+
              310nF

When you have 2km of line, the Z looking into the line terminated by the network above, the network below is a reasonable fit to:

--[300R]--+--[1000R]--+--
          |           |
          +----||-----+
              220nF			
			
2km is a reasonably typical line length from the exchange to the Terminal.

We end up with: 

[ Zc ] ---+--- [ Line ] --- [ Zc ]

If you make the balance impedance , "==Zb", equal to the Network Impedance, then the Sidetone is quieter at long lines.

 
The caller's Sidetone will be quieter, so they speak louder. 

They speak quieter when there is more sidetone.

When a caller speaks, they hear their own voice, and this is via the jaw bone and via the air path. 

I remember STMR meaning "SideToneMaskedRating". 
			

[terminal]---+---[ line ]---[exchange]

            NTP
            <- Zc        <-Zn 
            Zn->         Zc-> 
			   
So try setting the balance impedance Zb equal to Zn so Side tone is quietest at 2km.			   


See Fig6 - Line impedance for minimum sidetone (Zso), p267 British Telecommunications Engineering. Vol 5 Jan 1987
Zso:-  

--[270R]--+--[1500R]--+--
          |           |
          +----||-----+
              180nF

It is unknown what Zc and Zb are used in modern Phones.

Set Exchange to Zc Zso - BTE. Vol 5 Jan 1987

This calculates Zc and Zb which are tabulated in the BTR1050 COMPLEX phone sensitivities.

So COMPLEX PHONE32 uses Zc = --[370R]--[620R||310nf]--- , and balance Z, ==Zb or Zso = --[270R]--[1500R||180nf]---

NOTE:OLDxx phones include le
NOTE:COMPLEXxx phones do not include le
Remove LE if first line is starts BT700
Near Phone Data:
freq ss sr zcm zca zbm zba

 Far Phone Data:
freq ss sr zcm zca zbm zba

 Phone Data for BT700 OLD40:
freq ss sr zcm zca zbm zba

 
PABX:
Make Zc of the exchange and Terminal, the Terminal Impedance below:-
--[370R]--+--[620R]--+--
          |          |
          +----||----+
              310nF

When you have 2km of line, the Z looking into the line terminated by the network above, the network below is a reasonable fit to:
--[300R]--+--[1000R]--+--
          |           |
          +----||-----+
              220nF			
			
2km is a reasonably typical line length from the exchange to the Terminal.

So make Zb = 
--[300R]--+--[1000R]--+--
          |           |
          +----||-----+
              220nF

SWITCH Delays:-
NF_loss, dB:
FN_loss, dB:
delay, milliseconds :

Far Termination should be p, or t or 6 :

when using t or 6 three different ways of calculating STMR are displayed. 

p for Phone
t for Stone Bridge + 600ohm
else 600 ohm termination or 600ohm Source.

NOTE: Analogue PABX used 3dB loss, but Digital PABX need the losses increased to 6dB due to the time switch delays. 8000 samples per second is 125us.

The delay due to digital switching, affects the Sidetone, so using trans PABX loss improves the stability.

Now Echo Cancellers are essential with delays of multiples on 20ms introduced by VoIP. Some Smartphones introduced 460mS delay.

The audio program Audacity allows 110ms, due to PC sound cards.

These calculations cannot be trusted if the delay is more than 1/( 3150Hz-2500Hz) = 1.5ms.

The calculations alias due to subsampling. Finer steps in frequency are required if the delays are large.

Set Exchange to Zc Zn - SIN 351 , SIN355 phone -+- 2kn Line - Exchange

Set Exchange to Zc Zso - BTE. Vol 5 Jan 1987

recalculate

Loudness Ratings for different line lengths and Terminations

Reproducing CATNAP example

A photocopy of some CATNAP output was found, with a diagram. Using the buttons below, setup the exchange and phone. 

[Phone OLD40]-[600Ohm   100dB Attenuator]
[Phone OLD40]-[370R+620R//310nf   100dB Attenuator]

Set Exchange to PhotoCopy - needs BT700 OLD40 phone to match LMeST,

Set Exchange to PhotoCopy - needs BT700 OLD40 phone to match LMeST, losses per Freq

Set Phones to OLD40 as used in PhotoCopy - needs BT700 OLD40 phone to match LMeST

recalculate

This reproduces the LMeST found on a photocopy of CATNAP output. So it is reasonable to suggest the other Loudness Ratings may reproduce CATNAP.

NOTE: LMe values

Phone Sensitivities

COMPLEX PHONE32
 freq    ss   sr   zcm  zca     zbm  zba
 200  -15.0  11.1  966   -8.4  1678  -15.8
 250  -12.7  13.3  953  -10.4  1633  -19.3
 315  -10.1  15.2  934  -12.7  1566  -23.5
 400   -7.9  16.0  906  -15.6  1472  -28.25
 500   -6.1  17.3  869  -18.4  1361  -32.9
 630   -4.6  17.8  819  -21.4  1225  -37.6
 800   -3.1  18.1  757  -24.2  1072  -41.9
1000   -1.5  18.4  693  -26.1   928  -45.0
1250   -2.0  19.2  628  -27.1   793  -46.8
1600   -1.9  20.8  561  -26.8   662  -47.3
2000   -2.5  20.4  510  -25.4   563  -46.2
2500   -3.0  19.2  469  -23.0   484  -43.8
3150   -1.1  19.3  438  -20.4   420  -40.2
4000  -18.4   8.7  414  -17.3   371  -35.6

BT700 OLD40
 freq    ss   sr   zcm  zca     zbm  zba
 200  -13.9   6.4 648.0 25.0 726.0 -81.0
 250  -12.2  12.1 624.0 17.2 744.0 -70.8
 315  -10.8  16.7 587.0 12.4 790.4 -65.0
 400  -10.0  19.2 557.0 11.0 884.0 -61.0
 500   -9.4  21.2 546.0 11.0 784.0 -52.0
 630   -8.0  22.1 542.5 11.2 775.5 -48.3
 800   -5.8  22.9 555.0 14.0 771.0 -47.0
1000   -1.8  22.4 576.0 14.0 711.0 -45.0
1250    1.3  22.3 597.0 12.0 666.0 -44.0
1600   -0.6  22.6 585.0 12.0 611.0 -43.0
2000   -2.0  18.0 624.0 15.0 570.0 -44.0
2500   -3.4  11.1 661.0 11.0 511.0 -42.0
3150   -1.7  16.4 611.0 13.1 471.5 -40.2
4000  -12.2   4.2 699.0 14.0 431.0 -38.0

TABLE1 from  "p267 British Telecommunications Engineering. Vol 5 Jan 1987"
Four-Wire Switch Impedances
# freq ZC.r ZC.i ZSO.r ZSO.i
1 200 1280 -293 1057 -220
2 250 1237 -349 1022 -259
3 315 1174 -411 973 -300
4 400 1087 -469 909 -335
5 500 987 -510 839 -358
6 630 869 -531 762 -368
7 800 744 -524 683 -363
8 1000 637 -494 616 -348
9 1250 547 -447 556 -325
10 1600 469 -387 500 -297
11 2000 419 -333 458 -270
12 2500 383 -284 423 -243
13 3150 357 -241 393 -218
14 4000 338 -206 369 -196

Graphs of complex Z using the networks on this page.

Conclusion

Using the 2x2 matrices and other functions, the telephone connections can be explored.