Secondary-referred resistance calculation help

[Gregwor]

I’m trying to put together a Google Sheets calculator to speed up the process of figuring out which power transformer I want to use for projects. Basically I want to be able to enter spec sheet info and then it calculate estimated/rough minimum and maximum AC and DC voltages due to potential fluctuating wall voltages. This way I can ensure I will stay within device limits (example: drop-out voltages). I stumbled upon a hiccup and thought I’d reach out for help.

When trying to estimate/calculate the secondary-referred resistance (Rs), my numbers weren’t matching up. So I tried different calculation methods. Now, I know that I can’t expect perfect results using Schade's equation, but I was hoping to get in the ballpark and forge onward. After checking my formulas and calculations over and over to the best of my ability, I turned to chatgpt AI to see if it could help. After a little back and forth with the AI, I got the following calculations. The problem is that all 3 methods returned drastically different results as shown below.
Thank you in advance as I understand this is in depth and I hope the formulas below are easy enough to digest as it’s hard to write formulas on the forum.


The following calculations include the given specifications:

   Hammond 372HX

   Transformer VA for HT winding = 138
             (calculated using ohms law 600V * 230mA = 138 VA)
   Current rating for HT winding (I full load​) = 230mA
   Primary full load VAC = 120V
   Primary no load VAC = 120V
   Secondary full load VAC for entire CT winding = 600V (300-0-300)
   Secondary no load VAC for entire CT winding = 650.8V
   Two primary windings labeled for 120V each, wired in parallel:
      Primary winding DCR1 = 3.652 ohms
      Primary winding DCR2 = 3.968 ohms
   Entire secondary HT winding DCR = 77.16 ohms


Percentage Regulation Method:
       
Formula:
Rs = (Percentage Regulation × V full load ) /
        ((100 − Percentage Regulation) × I full load
       
Complete Formula:
Rs = (7.80% × 600) /
   (100 − 7.80%) × 0.230

Result:
Rs ≈ 311.67 ohms (based on the no-load percentage regulation and full-load conditions)

Equivalent Circuit Method:
       
Formula:
Rs = R reflected load − R load​
       
Complete Formulas:
N = V primary no load / V secondary no load
   = 120 / 325.4​
   = 0.369
           
R eq-primary = R primary DCR1 + R primary DCR2
   = 3.652 + 3.968
   = 7.62

R eq-secondary = R secondary DCR / 4
   = 77.164 / 4
   = 19.291
​
R reflected load = (N^2 x R eq-secondary / 2) + R eq-primary
             = (0.136 x 19.291 / 2) + 7.62
                       = 1.31 + 7.62
                       = 8.932

Rs = R reflected load − R load​

Result:
Rs ≈ 6.817 ohms (using the equivalent circuit approach and no-load conditions)

Adjusted Secondary Resistance Method:
       
Formula:
Rs = R sec / 4 + R pri (V sec / V pri)^2

Complete Formula:
Rs = 77.16 / 4 + 7.62 (150 / 120)^2

Result:
Rs ≈ 31.243 ohms (using the adjusted secondary resistance and the formula)


So, the 3 results are:

Rs ≈ 311.67 ohms (based on the no-load percentage regulation and full-load conditions)
Rs ≈ 6.817 ohms (using the equivalent circuit approach and no-load conditions)
Rs ≈ 31.243 ohms (using the adjusted secondary resistance and the formula)

Can anyone shed some light on this?

Thank you in advance!

Greg

[PRR]

> voltages due to potential fluctuating wall voltages.

They will be in proportion, near enuff.

if 120V AC makes 12V DC then
130V AC makes 13V DC
105V AC makes 10.5V DC

Schade should work if you squint the too-small curves.

PSUD has a 20+ year record of practical results while CheatAI has been spewing porn for only 20 months. I know which one I like.

[HotBluePlates]

... I got the following calculations. ...

From where, the chatbot?  I doubt it was trained on RDH4.  So if we're following Schade's steps in RDH4, then please point us to pages.

... The problem is that all 3 methods returned drastically different results as shown below. ...

Whether Human or Chatbot, simply performing steps without understanding seems unlikely to succeed.

  > "Percentage Regulation Method"

Your 1st section cribs specs from Hammond.
But the 2nd section assumes a "7.8% regulation" arbitrarily and got a much higher estimated winding resistance.
This means the Hammond has much tighter regulation than 7.8%, because it uses a smaller winding resistance (77Ω vs 300Ω).


  >"Equivalent Circuit Method"
  >"Adjusted Secondary Resistance Method"

I don't even know what these are.  They're a bunch of B.S. numbers without any particular meaning or purpose.