Judging by the number of views on a post related to numerical cable equalization, on the High Speed E2E forum (more than 3,700 at last count!), I would guess that it’s a pretty interesting topic for many folks. Since TI is one of the leading manufacturers of current feedback amplifiers (CFA), the workhorses for cable equalization, this twopart blog is devoted to giving you everything you need to implement your custom design, with a list of best devices to use and simulation techniques to boot. In this post, I will present some background information on equalization and a spreadsheet that allows you to automate the design. In part 2, we will use TINA to simulate the design and look into methods of improving the stability of the stage.
Xavier Ramus, a frequent contributor to Analog Wire, does a great job in his Application Note, A Numerical Solution to an Analog Problem, of explaining how to use a spreadsheet like Excel to do the hard work of placing the poles and zeros of Figure 1 high frequency (HF) gain boost banks (R_{A}, C_{A}, etc.) at the right frequencies to match the cable so that the cable + amplifier exhibits a flat frequency response. The reason this task is not trivial is these poles and zeros interact with each other if they are spaced close enough, making it difficult to “tune” the total arrangement. With the spreadsheet you can manipulate the component values and see their effect instantaneously.
Figure 1: Typical equalizer schematic where R_{A}, C_{A}, etc. boost gain at high frequency
In the below Excel file, I have implemented the spreadsheet that Xavier has explained. It is set up for four boost banks (R_1, C_1 through R_4, C_4) capable of 25dB of boost. For more boost or longer cable lengths, you can cascade more identical stages. The spreadsheet has an entry for the number of stages “N” in cell M6, default set to “2”. This enables you to increase the total boost (e.g. 50dB of boost for two cascaded stages, etc.) for longer cables. For additional information, check out the below PowerPoint.
http://e2e.ti.com/cfsfile.ashx/__key/communityserverblogscomponentsweblogfiles/0000000325/3808.CableEqualization101Spreadsheet_2D00_Part1.xlsx
http://e2e.ti.com/cfsfile.ashx/__key/communityserverblogscomponentsweblogfiles/0000000325/6204.CableEqualization101PowerPointPart1.pptx
Earlier I mentioned that CFA is the architecture of choice for an equalizer. The reason is that the high frequency noise gain (1+R_{F}/Z_{G} where Z_{G }is the total impedance from the inverting input to ground) increase that you need for equalization has much less unwanted impact on loop gain (and subsequently closed loop response) for a CFA than for the traditional voltage feedback topology. Furthermore, a CFA with lower internal buffer output impedance (R_{I},_{ }see OA13) holds an advantage because of the same reason. Table 1 below is a list of TI CFA amplifiers with pertinent specs, ordered from lowest R_{I} to highest:
Device 
R_{I} (Ω) 
R_{F }nominal (Ω) 
Large Signal BW (Av=+2) (MHz) 
11 
768 
880 

15 
1k 
300 

29 
402 
450 

29 
402 
400 

30 
390 
1,000 

30 
549 
400 

30 
402 
675 

30 
402 
670 

30 
560 
750 

37 
402 
440 

180 
390 
400 

500 
1.2k 
100 

N/A 
237 
720 
Table 1: TI High speed CFA portfolio
Once you’ve selected a proper device from Table 1, enter its recommended feedback resistor “R_{F} nominal” value in Excel cell C6. To get your design (Excel row 6 final values), follow the instructions in the PowerPoint file (pages 49) and use Excel Solver function to minimize the difference between the computed response of your amplifier from the computed attenuation of your cable (the Excel file is already set up for that in Column P). You can find “minimize” (called “min”) in Excel under data > solver. The solver function does this by manipulating the values of gain elements in row 6 to find the best solution. You do this at low frequency and work your way up to the highest frequency of interest, and when you’re done you will end up with a plot in Excel, such as the one in Figure 2 where the amplifier response overlaps the cable attenuation plot (up to 100MHz and with ~55dB of boost from 2 identical cascaded stages).
Figure 2: Amplifier gain superimposed on cable loss
This allows you to equalize the losses in your cable for a flat overall (cable and amplifier) response. Figure 3 shows the schematic of the circuit designed by Excel:
Figure 3: Excel Solution_ One of Two LMH6733 Stages Used as Cable Equalizer
Stay tuned for Part 2 (http://e2e.ti.com/blogs_/b/analogwire/archive/2013/06/05/cableequalization101simulatingthedesignandimprovingstability.aspx), where I will discuss how TINA can be used to simulate this circuit in order to shed more light on its stability. In the meantime, please use the comments field below to fill me in on some of your biggest challenges with numerical cable equalization. Also, let me know if you found this useful and if there is additional information you feel I should cover in Part 2.