In “Cable Equalization 101 - Automating your design,” we saw how a spreadsheet like Excel can be used to generate an equalization design rather painlessly, and we obtained the design in Figure 1 below. Here, we will use simulation to make sure the design is stable.
Figure 1: Excel solution found in Part 1_ one of two LMH6733 stages used as cable equalizer
Since Excel doesn’t know about the non-ideal behavior of the amplifier you have chosen, it is wise to test the results of the equalization design using simulation. Without a good simulation model for the cable, one would have to rely solely on the amplifier open loop response simulation. It turns out we have the means to investigate this stability criteria for the CFA in TINA as explained further below.
From OA-13, CFA Loop Gain Analysis, the CFA transfer function shown below in Equation 1, the stability criteria states that at the frequency where Z(s) (Transimpedance Gain) intercepts Feedback Transimpedance (Rf + RI (1+ Rf/ Rg)), the phase shift should be 135˚ or less (for 45˚ phase margin). We can investigate this intercept point in TINA to increase the confidence in the design.
Equation 1: CFA transfer function
For a cable equalizer, replace Rg in Equation 1 with the complex impedance ZG, which is the parallel combination of all boost bank elements, R1, C1, R2, C2, etc., (including RG) shown in Figure 1. We rely on the amplifier (LMH6733) TINA file to model the behavior of Z(s) over frequency and also the fixed value of RI built into the model. And of course Rf is the recommended feedback resistor for this particular CFA, which is what was used in the Excel file to produce the Figure 1 solution to begin with.
Here is how we can get these pertinent plots over frequency to show in TINA for us to conduct our stability analysis:
a) Feedback Transconductance (1 / Transimpedance) is the current flow into the inverting input (I_Rsense) in response to output (OUT1), with the loop open. Figure 2 below includes L_Large and C_Large which open the loop in AC (where we are concerned about stability and response) but leave it closed for DC to set the operating point.
b) Z(s) is “Amp_out / I_Rsense” (TINA can easily do the arithmetic on waveforms!)
Figure 2: TINA tricks to open the loop and to sense inverting current
So, we have everything at our disposal to investigate the point of intercept of Z(s) and feedback Transimpedance graphically using TINA. See Figure 3 below for three values of resistance R1, chosen as the bank element most likely to affect stability, in order to find the optimum value of R1.
Figure 3: Open loop gain and feedback transimpedance plot intercept for three values of R1
From Figure 3, the direct Excel solution (R1= 1ohm) would be unstable because of the 40dB/decade rate of closure of the two plots (this has to do with excess phase shift around the loop). Increasing R1 to 50ohm would be excessive and would limit the frequency response, while R1=10ohm is ideal because it places a Feedback Transimpedance pole at the intercept frequency and yield about 45˚ of phase margin.
We were able to take the Excel design one step further and verify against the device’s TINA model to anticipate real world issues with the boost in noise gain we have implemented. Bench verification and optimization of the design with the actual intended cable is the next step to complete the process.
I’ve included the TINA simulation file link for those of you who like to tinker with it and test other possibilities.
Hope you enjoyed this blog and found it useful. Please let me know if there any questions!