[ §9 · calculators · CT timing ]

Current transformer timing delay

How much time the current transformer itself costs, and with which sign. A CT gives lead, not delay, which is counter-intuitive: the lead you need from the inductor goes down by this amount rather than up. The site's phase-lead budget counted it as a plus until we worked this out.

second stage corefirst stage corefirst stage turnssecond stage turnssecond stage core A_L · nH/turn²first stage core A_L · nH/turn²or L_m measured · µHburden, total · Ωfrequency · kHzlead required · ns

L_m of second stage 920 µH (from A_L)φ of second stage 0.079° = 0.45 ns First stage, loaded by the second stage input: reflected burden 9.75 mΩ φ of first stage 0.001° = 0.007 ns TOTAL from the CT 0.45 ns of LEAD Sign: this is lead, not delay.So the lead asked of the inductor GOES DOWN: 314 - 0.45 = 313.55 ns 0.1 %: negligible.At a low burden the magnetising term all but vanishes. At a 51 Ω burden this would be 5.85 ns, which is whythe term mattered with the stock burden and does not now.

formula

I_burden = (I_pri/N) · jωL_m / (jωL_m + R)
phase = 90° - arctan(ωL_m/R) = arctan( R / (ω·L_m) )   > 0  ⇒ LEAD
t = φ / (360°·f)        L_m2 = A_L2 · N₂²      L_m1 = A_L1 · N₁²
the first stage is loaded by the second's input, i.e. R/N₂², so its share is nil

limits

Measure instead of computing where you can. Open the primary side of the second stage and measure the inductance of its secondary: that is L_m. The measured field takes priority over A_L.

Measuring the time directly is possible but needs a reference channel: a second CT with a high ratio and a low burden, so its own error is small, or a current clamp. Then compare its zeros against the voltage on the working burden. Going through L_m is more practical.

Only the magnetising term matters. The CT's leakage sits inside this same term rather than beside it. The signal is sensed across L1 + R, which puts the leakage upstream of the sense point and under 920 µH of L_m. Moving it from 0 to 1 µH shifts the total lead by 0.000085°. So this is the full figure, not a lower bound. The 13° quoted earlier belonged to a topology that is not on the board.

The wiring between the sense point and the burden is not included. It adds straight to L1: forgetting 0.3 µH of it at a 3.9 Ω burden turns a 55.5° lead into 59.4°, 7 % too much. See the current transformer page.