PGA460-Q1: Figure of merit

Hello Cherry,

Thanks for the clarification, the coefficients generated automatically for frequencies below 80kHz are dependent on the center frequency (FREQ) and the bandwidth of the filter (BPF_BW setting).

The linked thread has the formulas used for these instances, here is the required snippet from that thread:

The Band-Pass filter works based on digital coefficients B1, A2 and A3. These are calculated based on the burst frequency (FREQ parameter) and Band-Pass bandwidth (BPF_BW parameter). The A2 coefficient is calculated as following:

• A2= (0.6036*cf^2) +( 2.7401*cf) -32615           ….           For BPF Bandwidth  2kHz.
• A2= (0.5999*cf^2) + (2.7217*cf) -32415           ….           For BPF Bandwidth  4kHz.
• A2= (0.5965*cf^2) + (2.6791*cf) -32217           ….           For BPF Bandwidth  6kHz.
• A2= (0.5928*cf^2) - (2.6726*cf) -32024            ….           For BPF Bandwidth  8kHz.

Where “cf” is the filter center frequency in kHz (Defined by the FREQ parameter).

The B1 and A3 coefficients are calculated purely based on the filter band-width:

• B1=199.7*bw+12
• A3=-399.3*bw+65512

Where “bw” is the filter band-width in kHz (Defined by the BPF_BW parameter). Since there will be only four B1 and four A3 coefficients it might be worth to simply store the values instead of doing the calculation. In this case, below are listed the correct values for the B1 and A3 coefficients:

• B1 = 409 ; A3 = 64718        ….           For BPF Bandwidth 2kHz.
• B1 = 813 ; A3 = 63909        ….           For BPF Bandwidth 4kHz.
• B1 = 1213 ; A3 = 63111       ….           For BPF Bandwidth 6kHz.
• B1 = 1607 ; A3 = 62322      ….           For BPF Bandwidth 8kHz.

It is important to note that these are scaled-up coefficient values. The true B1, A2 and A3 values are always low number values (typically < +/- 2). The scaling is the following:

• B1 = B1_real * 2^16
• A2 = A2_real * 2^14
• A3 = A3_real * 2^16

In the digital filter implementation the values are scaled-down right before their use. IMPORTANT: The above coefficient formulas are only applicable for a sample rate of 1us.

I hope this helps!

Best,

Isaac