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Cable equalization 101 – Automating your design (Part 1)

Hooman Hashemi
Other Parts Discussed in Post: LMH6733

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 two-part 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 (RA, CA, 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 RA, CA, 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/cfs-file.ashx/__key/communityserver-blogs-components-weblogfiles/00-00-00-03-25/3808.Cable-Equalization-101-Spreadsheet-_2D00_-Part-1.xlsx

http://e2e.ti.com/cfs-file.ashx/__key/communityserver-blogs-components-weblogfiles/00-00-00-03-25/6204.Cable-Equalization-101-PowerPoint-Part-1.pptx

Earlier I mentioned that CFA is the architecture of choice for an equalizer. The reason is that the high frequency noise gain (1+RF/ZG where ZG 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 (RI, see OA-13) holds an advantage because of the same reason. Table 1 below is a list of TI CFA amplifiers with pertinent specs, ordered from lowest RI to highest:

Device

RI (Ω)

RF nominal

(Ω)

Large Signal BW

(Av=+2)

(MHz)

THS3201

11

768

880

THS3001

15

1k

300

OPA695

29

402

450

OPA2695

29

402

400

LMH6733

30

390

1,000

LMH6738

30

549

400

OPA694

30

402

675

OPA2694

30

402

670

LMH6703

30

560

750

OPA3695

37

402

440

LMH6714 / LMH6722

180

390

400

LMH6723/ LMH6724

500

1.2k

100

LMH6702

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 “RF nominal” value in Excel cell C6. To get your design (Excel row 6 final values), follow the instructions in the PowerPoint file (pages 4-9) 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/cable-equalization-101-simulating-the-design-and-improving-stability.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. 

Anonymous

  • Dear Hooman

    My apologies for the late reply, I have been in hospital for the last 3 months and only now back on my feet.

    I am returning to work soon in a limited capacity so that will be an ideal time to experiment with this.

    I have ordered 10  LMH6733 chips and will proceed using the cascaded design and values which you suggest.

    My thanks to you for your assistance in this matter - as you can tell I am a technician rather than an engineer and more used to

    faultfinding than design but I'm sure with some perseverance I will get there.

    Best regards

    Neil

  • Hello Neil,

    Part 2 is already posted to E2E. Here it is:

    e2e.ti.com/.../cable-equalization-101-simulating-the-design-and-improving-stability.aspx

    Part 2 deals with simulation techniques using Tina-TI to sanity check the design that the Excel file in this post produces, for stability.

    Regarding equalization of video (limited to 10MHz?) with 1km of RG59:

    Assuming 3.6dB / 100m @ 10MHz loss (from: www.belden.com/.../8241.pdf), you'd need 36dB of boost for 1km.

    That seems doable with 2 stages (25dB/ stage limit).

    If I plug in 36dB into the Excel cell N6 (loss at 10MHz), and go through the steps of "solving" column P from top to bottom for "minimum" (as described in this post), I get the following design for you particulars:

    2 cascaded LMH6733 stages with identical values for each as shown:

    RF      RG        R_1        C_1(pF)   R_2 C_2(pF)      R_3 C_3(pF)     R_4    C_4(pF)

    390      722        1        233           420 608             1        230             1,306    2,416

    I've not done any sanity checking of this design. May be you can read Part 2 and do that for yourself? :-)

    Regards,

    Hooman

  • Hi Hoosman

    I eagerly await part 2 as I am still struggling to achieve acceptable results with video over 1000M of RG59 - maybe just not possible?

  • I'm not familiar with the Power application you have noted.

    You must be referring to the way Excel can be used to "minimize" a function (under Data, Solver Menus), which can be set up to be the difference between the expected response and what the circuit actually does, by varying a selected list of cells which affect the response. In this particular case, the function which is minimized is the "square" of this difference to be a true measure of difference regardless of sign (+ or -). Furthermore, the function accumulates the differences as you move up in frequency so that you don't minimize the difference at one frequency and throw-off the solution at all lower frequencies. The complex number capabilities noted in the PowerPoint attached may be a useful reference when dealing with arithmetic like that in Excel.

  • This would also be a great way to simulate skin and vicinity effect copper losses for power magnetics, especially for PFC chokes with both mains and varying switch frequency components.