AN84

AN84 SILABS | Alldatasheet

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Figure 3. Model Figure 3. In an ideal system, the analog hybrid yields include the ac termination and line. Figure 4. HL(ω)–1 Model perfectly cancels the transmit signal. where gd is the group delay.

2 ZACT

Rev. 0.6 3 1.2. Digital Hybrid Calculation Tool Silicon Labs has developed a useful graphical user interface tool (shown in Figure 5) that will assist in calculating the coefficients to use with the digital hybrid in the Si305x DAA product family. The tool allows the user to enter the reference termination of the central office (in an R + R||C fo rmat) and the model for the phone line between the DAA and the central office. The line can be represented by one of the EIA models, shown in " Appendix C—EIA Line Models" on page 24, or as a specified length of wire. The software then executes the Matlab code found in " Appendix A— Sample MATLAB Code" on page 7, which graphically shows the expected trans-hybrid response of the digital hybrid and lists the best hybrid coefficients to use given the line characteristics. Three graphs are shown in Figure 6. An echo graph is created by intentionally mismatching the 600 Ω ac termination with the TBR21 mo de CO termination. The digital hybrid response is the 8-tap FIR filter response calculated using the sample code found in Appendix A. The cancelled graph is obtained by adding the echo and the digital hybrid response. The digital hybrid response looks very similar to an echo. Figure 7 shows the phase of the echo and the digital hybrid response. The phase of an echo and the digita l hybrid have the opposite polarity. Figure 8 compares the rejection in dB with and without the digital hybrid. By properly using the digital hybrid, near-end echo cancellation has increased by approximately 20 dB. To use the Digital Hybrid Calculation Tool, simply enter the ACIM value recommended in Table 13 of the Si3050 datasheet into the ACIM control. This value determines the impedance presented by the DAA to the line. It is governed by the region in which the application will be deployed. Next, enter values for R1 and R2 in ohms and C in farads into the appropriate controls. These values will represent the im pedance presented by the central office to the line. This value is also governed by the region in which the applicat ion will be deployed. Also, select the line-side device used in the application in the pull-down box. Finally, select the line model to be used that will most closely model the line connecting the DAA to the central office. This is done by either picking a specific EIA line model or by specifying a wire gauge and length. Once this is complete, hitting the "CALCULATE" button will generate the coefficients that provide the best performance. For example, if we assume that an application will be deployed within the U.S., we enter a 0 for the ACIM value. Also, the central office impedance in the US is 900 Ω in series with 2.16 µF. To enter this information in the GUI, we enter 900 for R1 and a fairly large value for R2, since it is not present. For this example, the value of 100,000 Ω was used. For the C value, we enter 2.16e-6 since the expected units are farads. Also, for this example, we use an EIA model of 0. This means essentially no loop length, and the central office impedance is connected directly to the application. Now, the "CALCULATE" button is pressed, and the resulting coefficients, 0xF8, 0xF9, 0x03, 0xFE, 0xFE, 0x00, 0xFE, and 0x00, are generated.

Figure 5. Digital Hybrid

response to be represented in the z-domain. calculating the hybrid coefficients. use for different line conditions. Figure 6. Echo

Rev. 0.6 7 APPENDIX A—S AMPLE MATLAB CODE A sample MATLAB program for use in setting the hybrid coefficients is shown below. The code takes the ACIM (Register 30) setting and line model as an input and outputs the best coefficient for the digital hybrid to match the line. function hdh = dig_hybrid(ACIM, R1line, R2line, Cline, HtMag, HtPhase, HrMag, HrPhase); % hdh = dig_hybrid(ACIM, R1line, R2line, Cline, HtMag, HtPhase, HrMag, HrPhase); % This function calculates the coefficient values for the digital % hybrid given a R1+R2||C model for the line. % ACIM : register setting of the AC termination % R1line : line R1 % R2line : line R2 % Cline : line C % HtMag : Transmit path response % HtPhase : Transmit path response % HrMag : Receive path response % HrPhase : Receive path response % hdh : digital hybrid coefficients Nact=ACIM+1; if(R1line==0), R1line=eps; end if(R2line==0), R2line=eps; end if(Cline==0), Cline=eps; end %eps is the smallest value after 0 % Set sample rate and frequency grid fs=16000; f=[eps:1:7999]; w=2*pi*f/fs; %%%%%% Transmit path (Ht) Ht = HtMag .* exp(j*HtPhase) %%%%%%% Receive path (Hr) Hr = HrMag .* exp(j*HrPhase)

8 Rev. 0.6 %%%%%%%%%% Near end echo (H2) % Calculate Zline Zcline=1./(j*2*pi*f*Cline); Zline=R1line + R2line.*Zcline./(R2line+Zcline); % Calculate Zref, assume perfect ACT R1ref=[eps eps 270 220 370 320 370 275 120 350 eps 600 900 900 600 270]; R2ref=[600 900 750 820 620 1050 820 780 820 1000 900 1e9 1e9 1e9 1e9 750]; Cref =[eps eps 150 117 310 230 110 132 110 210 30 2160 1000 2160 1000 150]*1e-9; Zcact=1./(j*2*pi*f*Cref(Nact)); Zact=R1ref(Nact) + R2ref(Nact).*Zcact./(R2ref(Nact)+Zcact); C9r=0*1e-9; Ycact2=(j*2*pi*f*C9r); Zact=1./(1./Zact + Ycact2); %%%%% HL=2*Zline./(Zact+Zline); HL(1)=0; % Add extra group delay to match measurements gde=-0.225; Hd=-Ht.*Hr.*(HL-1).*exp(j*2*pi/16000*gde*[0:length(Ht)-1]); Hd=[Hd conj(fliplr(Hd))]; % Estimate impulse response to match hd=real(ifft(Hd)); % Truncate coefficients and express in [0 255] hdh=round(hd(5:12)*64); ind=find(hdh<0); hdh(ind)=hdh(ind)+256; echo = Ht.*Hr.*(HL-1).*exp(j*2*pi/16000*gde*[0:length(Ht)-1]); hyb_coef = [0 0 0 0 hd(5:12)]; dig_hyb = freqz(hyb_coef,1,w); figure plot(f,abs(echo),'-',f,abs(dig_hyb),'-.',f,abs(echo+dig_hyb),':') axis([0 4000 0 0.4]) legend('echo','digital hybrid response','cancelled signal')

Rev. 0.6 9 xlabel('frequency') ylabel('echo') figure plot(f,angle(echo),'-',f,angle(dig_hyb),'-.') axis([0 4000 -pi pi]) legend('echo','digital hybrid response') xlabel('frequency') ylabel('echo') figure plot(f,20*log10(abs(echo)),'-',f,20*log10(abs(echo+dig_hyb)),'-.') axis([0 4000 -42 0]) legend('echo','cancelled signal') xlabel('frequency') ylabel('rejection')

used to calculate the hybrid coefficient. The remaining columns display the hybrid coefficients (Registers 45–52). Table 1. ACIM = 0000 and CO Termination = 900 Ω + 2.16 µF Table 2. ACIM = 0000 and CO Termination = 600 Ω

Table 3. ACIM = 0000 and CO Termination = 1200 Ω + 376 Ω + 112 nF Table 4. . ACIM = 0000 and CO Termination = 150 Ω + 510 Ω + 47 nF

Table 5. ACIM = 0000 and CO Termination = 220 Ω + 820 Ω + 150 nF Table 6. ACIM = 0000 and CO Termination = 600 Ω + 1.5 µF

Table 7. ACIM = 0010 and CO Termination = 220 Ω + 120 Ω + 115 nf Table 8. ACIM = 0011 and CO Termination = 220Ω + 820 Ω + 115 nF

Table 9. ACIM = 0100 and CO Termination = 370 Ω + 620 Ω + 310 nF Table 10. ACIM = 0100 and CO Termination = 220 Ω + 820 Ω + 120 nF

Table 11. ACIM = 0101 and CO Termination = 300Ω + 1000 Ω + 220 nF Table 12. ACIM = 0101 and CO Termination = 370 Ω + 620 Ω + 310 nF

Table 13. ACIM = 0101 and CO Termination = 270 Ω + 750 Ω + 150 nF Table 14. ACIM = 1010 and CO Termination = 200 Ω + 560 Ω+ 100 nF

Table 15. ACIM = 0000 and CO Termination = 900 Ω + 2.16 µF Table 16. ACIM = 0000 and CO Termination = 600 Ω

Table 17. ACIM = 0000 and CO Termination = 1200 Ω + 376 Ω + 112 nF Table 18. ACIM = 0000 and CO Termination = 150 Ω + 510 Ω + 47 nF

Table 19. ACIM = 0000 and CO Termination = 220 Ω + 820 Ω + 150 nF Table 20. ACIM = 0000 and CO Termination = 600 Ω + 1.5 µF

Table 21. ACIM = 0010 and CO Termination = 220 Ω + 120 Ω + 115 nF Table 22. ACIM = 0011 and CO Termination = 220Ω + 820 Ω + 115 nF

Table 23. ACIM = 0100 and CO Termination = 370 Ω + 620 Ω + 310 nF Table 24. ACIM = 0100 and CO Termination = 220 Ω + 820 Ω + 120 nF

Table 25. ACIM = 0101 and CO Termination = 300 Ω + 1000 Ω + 220 nF Table 26. ACIM = 0101 and CO Termination = 370 Ω + 620 Ω + 310 nF

Table 27. ACIM = 0101 and CO Termination = 270 Ω + 750 Ω + 150 nF Table 28. ACIM = 1010 and CO Termination = 200 Ω + 560 Ω + 100 nF

Figure 9. EIA Line Models

26 AWG

24 AWG

26 AWG6 kft

Rev. 0.6 25 DOCUMENT CHANGE LIST Revision 0.3 to Revision 0.4 „ Added Figure 5 on page 4. „ Added " Appendix C—EIA Line Models" on page 24. Revision 0.4 to Revision 0.5 „ Updated Figure 5 on page 4. „ Added Tables 17–32 (information for Rev E and later versions of the Si3019). Revision 0.5 to Revision 0.6 „ Updated "1.2. Digital Hybrid Calculation Tool" on page 3. „ Updated Figure 5 on page 4. „ Updated " Appendix B—Hybrid Coefficient Lookup Tables" on page 10.

26 Rev. 0.6 CONTACT INFORMATION Silicon Laboratories Inc.

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