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TLV320AIC3256: Pure Path Studio

user4834077
Prodigy 235 points
Part Number: TLV320AIC3256

Hi,

 I want to use the Biquad Filter Design Tool in the  PurePath Studio. I choosed Equalizer(Q factor) and other factors as shown in Fig.1. And then it produced a frequency responce graph  as shown in Fig.2. I wan to know the functional relationship about the X-axis(frequency) and Y-axis(Gain) . Is there someways?

Best regards!

Maolin. Shi

   Fig.1

Fig.2

  • 0
    TI__Expert 6440 points

    Hi Maolin Shi,

    In most cases, the filter design tool achieves a filter response that matches the user programmed values.

    However in some cases, the user settings are not perfectly realizable. The bi-quad filter coefficients have a pre-determined fixed point representation with a certain number of bits used for signed integer representation and the rest used for fractional representation. When the computed filter coefficients are beyond what is represent-able, the tool scales the coefficients down to bring it within range. 

    The scale factor used by the tool is listed in the last column ( as shown in Fig. 1 of your thread). As you can see, in most cases it is 1.0 (which means no scaling). In this particular case, the scale value is 0.86. It is a linear value and the effective dB gain after applying the scale can be calculated as follows:

    new_gain = 20*log10(<scale>*10^(<user_gain>/20)) = 20*log10(0.86*10^(20/20)) = 18.68 dB

    To obtain a full 20 dB gain, a shift-scale component can be added after the biquad to reverse the scaling done in the biquad.

    To reverse the gain, the shift scale component should have an effective gain of 1/0.86 = 1.1628.

    A gain of 1.1628 can be achieved by setting a shift of 1 (i.e. multiply by 2) and scale of 1.1628/2 = 0.5814.

    If there are multiple bi-quads that have gain scales less than 1.0, then the recommended procedure is to combine all the scales into one scale by multiplying all the scales (eff_scale = scale1 * scale2 * ...) and to use the shift-scale component to reverse the scaling done in the bi-quads by programming the effective gain to 1/eff_scale.

    Best Regards.

     

     

  • 0 in reply to Diljith
    Prodigy 235 points

    Hi,  Diljith,

    I understand what you said. 

    The situation  I has met is listed as follows:

    I know  clearly the real gain of 250Hz, 500Hz, 1KHz, 2KHz, 3KHz, 4KHz, 6KHz, 8KHz. I want to achieve the real gain  by adujsting the multiple bi-quads. There are two impact factors has to be considered: The first is scale factor as what you said and I has know how to solve it. The second is the bandwidth or Q factor of the target frequency.  It influences the gains of other frequency points. Now I has fixed the  bandwidth of every frequency point. And I want to get a realtionship about the real gains of every frequency point and the gains that has to be written to the multiple bi-quads. So I want to know the functional relationship  of  the functional relationship about the X-axis(frequency) and Y-axis(Gain)  so that I can quantifying the impact that the current   bandwidths of  every frequency point on other frequency points.

    Best regards.

    Maolin. Shi

  • 0 in reply to user4834077
    TI__Expert 6440 points

    Hi Maolin Shi,

    I think you are looking for the filter design equations used by PPS Bi-quad tool.

    If so, please refer to the application note Biquad Filters Application Note.pdf.

    In this application note, the equalizer design equations are based on the bandwidth parameter.

    Use the Q = BW/fc relation to convert between bandwidth and Q.

    The filter design equations describe the procedure for computing the five biquad coefficients –b0, b1, b2, a1, a2 – for each filter type. From the filter coefficients, you can compute the transfer function of the filter which allows you to compute the gain at each frequency point.

    Please let me know if this was the information that you were looking for.

    Best Regards.

  • 0 in reply to Diljith
    Prodigy 235 points

    Hi Diljith,

    Thank you very much! That‘ is exactly what I am looking for. 

    Best regards.

    Maolin. Shi

  • 0 in reply to user4834077
    TI__Expert 6440 points

    Glad to be of help!

    Best Regards.

  • 0 in reply to Diljith
    Prodigy 235 points

    Hi, Diljith

    I find the scale factor used by the PPS  is related to the Gain and Bandwidth.   Can you provide the formula?

    Best Regards!

  • 0 in reply to user4834077
    TI__Expert 6440 points

    Hi Maolin,

    I believe the equations are covered in the application note, which you probably have gone through already.

    There is an example worked out in Appendix A of the document. The first item is about the filter design aspect based on the different design equations. The second item in Appendix A explains the scaling. If b0 is greater than 1, then 1/b0 becomes the scaling factor. If b0 < 1 then the scaling factor is 1.0. The third and fourth items show how the final hexadecimal coefficients are computed after scaling.

    Let me know if you need additional information/clarification.

    Best Regards.

  • 0 in reply to Diljith
    Prodigy 235 points

    Hi, Diljith

    I has understood it. Thank you! I listed a biquad transfer function  as follows:

                b0 + b1*z^-1 + b2*z^-2
    H(z) = ------------------------                                  (Eq 1)
            1 + a1*z^-1 + a2*z^-2

    I want to know whether it 's  right.  Can you provide  detailed information about it ? 


    Best Regards!

  • 0 in reply to user4834077
    TI__Expert 6440 points

    Hi Maolin,

    The biquad transfer function equation appears correct to me. Do you see any issues with it? b0, b1 and b2 are the numerator coefficients and 1, a0 and a1 are the denominator coefficients. What other details would you like? Are you facing any issues while using the tool? Does you application require knowledge of the filter design implementation in the biquad tool. I have sent you a request to connect privately over E2E in case there are aspects of your application that you would not like to present in the forum.

    Best Regards.