AN84 datasheet(2/26 Pages) SILABS

2 / 26 page

AN84

Rev. 0.6

Figure 3. Model

A model of the DAA and the phone line is shown in

Figure 3. In an ideal system, the analog hybrid yields

perfect cancellation of the near-end echo from the

transmit path. A mismatch between the ac termination

and the load produces an echo that is not removed by

the analog hybrid. To increase the near-end echo

cancellation, the digital hybrid must equalize the

disparity between the impedance mismatch of the ac

termination and the line.

From the above model, the echo is equal to:

HL(ω) consists of the DAA’s ac termination in

combination with the impedance of the twisted pair

transmission line terminated at the central office (CO)

by a reference impedance. Figure 4 shows the analog

hybrid circuitry and the HL(ω) model expanded to

include the ac termination and line.

Figure 4. HL(ω)–1 Model

Substituting for HL(ω) in the equation results in:

If ZLINE and ZACT are matched, the analog hybrid

perfectly cancels the transmit signal.

Substituting this result into the echo equation yields:

The model for the HT(ω) and HR(ω) plays a critical role

in this calculation. The models are quite complex, and

sampled data of the models are necessary to calculate

the hybrid coefficients. Contact Silicon Labs to acquire

the sampled data of the HT(ω) and HR(ω) models.

A group delay, which was not illustrated in the model,

must also be taken into consideration. Internal DSP and

filters cause this delay. Taking the group delay into

account, the echo is equal to:

where gd is the group delay.

The digital hybrid must cancel the echo by intentionally

adding the negative of the echo. The HD(ω) should be:

R(ω)

T(ω)

D(e

ω)

at 16 kHz

L(ω)

DAC

at 16 kHz

ADC at

16 kHz

echo

T ω

() H

L ω

()

R ω

()

T ω

() H

R ω

()

–

T ω

() H

R ω

()

L ω

() 1

–

[]

ACT

LINE

–

ZLine

ZLine ZACT

----------------------------------

–

ZLine ZACT

–

ZLine ZACT

----------------------------------

echo

T ω

() H

R ω

()

ZLine ZACT

–

ZLine ZACT

----------------------------------

echo

T ω

() H

R ω

()

() 1

–

[]e

16000

---------------- gd

⎝⎠

⎛⎞

HD ω

()

T ω

()

–

R ω

()

() 1

–

[]e

16000

---------------- gd

⎝⎠

⎛⎞

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