======================MUTUAL_INDUCTANCE====================== _____________________________ ->()____________________________) Two Wires D_cm _____________________________ ->()____________________________) L_cm M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) ======================K_and_M====================== __ __ coef of coupling | |__ <-L-> __| | K = coef of coupling |__| | | |__| K = M/sqrt(L1*L2) | () () | \_/\_/\_/ L1 K = sqrt(1-Lclose/Lopen) M _ _ _ Lopen = L1*K / \/ \/ \ L2 Lclose =L1*(K^2 -1)*K __ | () () | __ | |__| |__| | if K=1 then M=sqrt(L1*L2) |__| |__| Lopen = L1 and Lclose =0 ======================INDUCTANCE_CANCELATION====================== __ Alignment | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | if L1 = L2 =M __ | () () | | | |__| |_____| then Lb=0 |__| __ | |__ _____ |__| | | | La = L1 + L2 +2*M |*() () | | if L1 = L2 =M \_/\_/\_/ L1 | then Lb=4*L La M _ _ _ | / \/ \/*\ L2 | K = ((La-Lb)/4)/sqrt(L1*L2) __ | () () | | K = M/sqrt(L1*L2) | |__| |_____| |__| ======================IN_TRANSFORMERS========================== Typical Transformer K '` V1 ___ o o____ V2 \ / L1 _ | | _ L2 / \/ \/ \ \_/\ /\_/ _ | | _ / \/ \/ \ \_/\ /\_/ V2=V1*N2/N1 _ | | _ / \/ \/ \ I1=I2*N2/N1 \_/\ /\_/ | | ____/ \____ V1= L1*di1/dt + M*di2/dt V2= L2*di2/dt + M*di1/dt M= K*sqrt( L1+L2) ======================IN_TRANSFORMERS========================== __ P =10 + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | (P/S)*VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ Typical Transformer Turn Ratio =P:S L2a _ _ _ L2b _ _ _ K = L1b/L1 = L2b/L2 = 99% /*\/ \/ \ /*\/ \/ \ (S/P)*VL1b M = K*sqrt(L1*L2) __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| S=100 0 0 \___/ |__| + VL2b - L1 L1a+L1b L2 L2a+L2b Turn Ratio P:S K coupling coeffecient L1b/L1 = L2b/L2 = 99% M Mutual InductanceK*sqrt(L1*L2) VL1 (dI1/dt)*L1 + (dI2/dt)*M*(P/S) VL2 (dI2/dt)*L2 + (dI1/dt)*M*(S/P) VL1/VL2 P/S ======================TRANSFORMERS====================== _ _ _ _ _ _ / \/ \/ \ / \/ \/ \ LE 1:N _| () () |_______| () () |______ o o_______ IF K -> 1 | \ / V1 LE |________ _ | | _ V2 L1 = LM | / \/ \/ \ _ _ _ | \_/\ /\_/ L2 = N^2*L1 LM magnetizing inductance / \/ \/ \ | _ | | _ __| () () |_| / \/ \/ \ 1 -K = LE/LM | \_/\ /\_/ | LM _ | | _ | / \/ \/ \ | \_/\ /\_/ | | | ________|_______________________/ \________