Transformer Inrush Current: Limiting a 40VA Transformer

transformer

Have you ever turned on a transformer and heard a loud humming sound? What about having a blown fuse or tripped circuit breaker? These signs can all indicate transformer inrush current.

Transformer inrush current describes a spike in current that occurs when you initially turn on your transformer. This spike can be up to 10 times higher than normal current. Why does inrush current occur?  It can happen because large transformers demand a huge amount of current when energized. Until the inductive resistance and magnetic field builds, they essentially act as short circuits. This explains why you can experience distorted sounds (such as humming or buzzing) or blow a fuse quite easily.

Problematic Effects of Transformer Inrush Current 

Inrush current in a transformer can cause several problems. Not only does it interfere with the operation of circuits, but it could result in detrimental effects to the transformer. The distortion of the volt or current waveform, known as harmonics, is another side effect of inrush current.  If not properly managed, inrush current could lead to failure of circuit components, shorten the operating life of the transformer, or even cause damage.

Let’s look at the figure below. If the AC wave is going through its zero value, the current drawn will be very high and exceed the saturation current (Figure 1). In this situation, transformer inrush current protection becomes necessary to keep the transformer functioning properly.

Transformer inrush current wave

Figure 1: A transformer draws inrush current that can exceed saturation current affecting the magnetic property of the core.

Solution to Transformer Inrush Current 

What’s a practical solution to this problem? Well, one convenient way to limit inrush current in a transformer is by using an NTC thermistor. The photo below shows an NTC thermistor placed in the circuit board to provide optimal inrush protection (Figure 2).

Transformer inrush current limiter in circuit

Figure 2: The NTC thermistor is placed in series with the input line to limit inrush current in a transformer.

Transformer Inrush Current Calculation 

Here at Ametherm, we have a calculation that we use to help our customers choose the right NTC thermistor part number. We thought we’d share this with you so you can do the math for yourself, if you feel so inclined.

The 7 step process below will walk you through the calculation we did for a 40VA transformer. You can apply these calculations to your own transformer as well. Simply sub in your own application characteristics (found in step 1) and follow the equations. If you’re ready, grab a pen and paper and let’s get started!

Step 1: Define the Characteristics of Your Transformer

The 40VA transformer has the following given values. If you are doing these calculations for your own application, these values will vary.

Given Values: 

  1. KVA or VA of transformer= 40VA
  2. Input voltage= 110VAC

Step 2: Write Inrush Current Assumptions

We will use the following assumptions throughout our calculations. Depending on the shape of your transformer, you will use either 10 or 30 in the first assumption (see note).

Assumptions:

  1. Inrush Current = 30 x Steady State Current (SSI)
  2. Maximum Tolerable Inrush Current = 1/5 of Inrush Current
  3. Frequency= 50Hz

Note:

  • Use 10 x SSI if the geometry of the core is rectangular.
  • Use 30 x SSI if the geometry is toroidal (i.e. donut shape).
  • These are typical values that we have seen based on scope traces.
  • The max tolerable inrush current reduces inrush current by 80.

Step 3: Calculate Steady State Current of Transformer

Now that we have the given values and assumptions for our application, we are ready to start the calculations. First, we will calculate the steady state current of the transformer during normal operation by using the given values found in Step 1.

Step 4: Calculate Inrush Current

Second, we are going to calculate the inrush current caused when the transformer is powered on. You can find an explanation of this calculation in Step 2.

Step 5: Calculate Inductive Impedance

Third, we are going to calculate the inductive impedance. This is the amount of resistance the coil and core present to the electrical current.

 

 

Step 6: Calculate the Energy

Next, we will calculate the amount of energy the thermistor needs to prevent it from self-destructing.

Step 7: Calculate Minimum Cold Resistance of Thermistor

Finally, we are going to calculate the minimum cold resistance of the thermistor.

Select the Correct NTC Thermistor  

Now that steps 1-7 are completed, you can use the voltage, SSI, and energy parameters to look up your data sheet on the chart below. The data sheet will direct you towards the correct part number for your thermistor.

Part
(pdf)
UL CSA R
@25°C
SSI
Max
Joules
(Max)
D Max
(mm)
T Max
(mm)
DIGIKEY MOUSER NEWARK
SL32 0R230 UL 0.3 30.0 100 31.0 6.0 995-SL32-0R230
SL22 0R516 UL CSA 0.5 16.0 160 22.0 6.0 570-1031-ND 995-SL22-0R516 72J6814
SL32 0R530 CSA 0.5 30.0 150 31.0 5.0 570-1056-ND 995-SL32-0R530 72J6840
SL32 0R536 CSA 0.5 36.0 150 31.0 5.0 570-1057-ND 995-SL32-0R536 72J6841
MS32 0R540 0.5 40.0 250 31.0 7.0 570-1013-ND 995-MS32-0R540 72J6618
MS35 0R550 0.5 50.0 500 37.0 9.0 570-1023-ND 995-MS35-0R550 72J6628
MS32 0R536 0.5 36.0 250 31.0 7.0 570-1012-ND 995-MS32-0R536 72J6617
AS35 0R550 0.5 50.0 800 36.0 8.4 570-1110-ND 995-AS35-0R550
AS32 0R536 UL 0.5 30.0 300 29.0 7.8 570-1103-ND 995-AS32-0R536-100
AS32 0R530 UL 0.5 30.0 300 29.0 5.3 570-1118-ND 995-AS32-0R530-100
SL22 0R712 UL CSA 0.7 12.0 120 22.0 6.0 570-1031-ND 995-SL22-0R712 72J6815
SL18 0R712 0.7 12.0 120 19.0 6.0 72J6807
SL32 1R030 UL CSA 1.0 30.0 160 31.0 5.0 570-1059-ND 995-SL32-1R030 72J6842
SL32 1R036 CSA 1.0 36.0 160 31.0 6.0 570-1060-ND 995-SL32-1R036 72J6843
MS32 1R036 1.0 36.0 300 31.0 7.0 570-1016-ND 995-MS32-1R036 72J6619
MS35 1R040 1.0 40.0 800 37.0 11.0 570-1025-ND 995-MS35-1R040 72J6629
SL15 1R010 UL 1.0 10.0 45 16.0 5.8 995-SL15-1R010 72J6767
SL22 1R020 UL CSA 1.0 20.0 65 22.0 6.0 570-1041-ND 995-SL22-1R020 72J6816
AS32 1R030 UL 1.0 30.0 300 30.0 8.0 570-1104-ND 995-AS32-1R030
AS35 1R040 1.0 40.0 800 36.0 8.5 570-1111-ND
AS32 1R036 UL 1.0 36.0 300 30.0 8.0 570-1119-ND 995-AS32-1R036-100
SL12 1R010 1.0 10.0 28 12.0 4.0 570-1077-ND 995-SL12-1R010
SL12 1R308 UL CSA 1.3 8.0 40 13.0 4.5 SL12-1R308-ND 995-SL12-1R308 72J6731
SL22 2R018 UL CSA 2.0 18.0 90 22.0 6.0 570-1044-ND 995-SL22-2R018 72J6826
SL32 2R023 UL CSA 2.0 23.0 250 31.0 6.0 570-1061-ND 995-SL32-2R023 72J6845
SL32 2R025 UL CSA 2.0 25.0 300 31.0 7.0 570-1062-ND 995-SL32-2R025 72J6846
SL10 2R005 CSA 2.0 5.0 30 10.0 5.0 570-1081-ND 995-SL10-2R005 72J6716
MS32 2R025 UL 2.0 25.0 300 31.0 10.0 570-1019-ND 995-MS32-2R025 72J6622
MS35 2R035 2.0 35.0 750 35.0 10.0 570-1027-ND 995-MS35-2R035 72J6631
AS32 2R025 UL 2.0 25.0 300 30.0 7.8 570-1105-ND 995-AS32-2R025
AS35 2R035 2.0 35.0 700 36.0 8.5 570-1112-ND
SL22 2R508 2.5 8.0 90 22.0 5.0 570-1045-ND 995-SL22-2R508 72J6827
SL22 2R510 UL CSA 2.5 10.0 90 22.0 6.0 570-1046-ND 995-SL22-2R510 72J6828
SL22 2R515 UL CSA 2.5 15.0 90 22.0 6.0 570-1047-ND 995-SL22-2R515 72J6829
SL18 2R508 2.5 8.0 90 19.0 5.1 SL18 2R508-B-ND 995-SL18-2R508 72J6810
SL10 2R505 UL CSA 2.5 5.0 30 10.0 4.5 570-1098-ND 995-SL10-2R505 72J6717
SL12 2R505 UL 2.5 5.0 36 13.0 5.0 995-SL12-2R505 72J6745
SL15 2R508 UL CSA 2.5 8.0 40 16.0 5.0 995-SL15-2R508 72J6780
SL15 2R509 CSA 2.5 9.0 40 16.0 5.0 570-1102-ND 995-SL15-2R509 72J6781
SL08 2R503 UL 2.5 3.0 10 8.0 4.0 570-1120-ND 995-SL08-2R503
SL15 2R507 UL 2.5 7.0 40 15.0 4.5 570-1072-ND 995-SL15-2R507
SL15 2R506 UL 2.5 6.0 40 15.0 4.5 995-SL15-2R506
MS35 3R030 3.0 30.0 750 37.0 10.0 570-1028-ND 995-MS35-3R030 72J6633
AS35 3R030 3.0 30.0 600 36.0 8.5 570-1113-ND 995-AS35-3R030
SL22 4R014 UL CSA 4.0 14.0 100 22.0 6.0 570-1050-ND 995-SL22-4R014 72J6833
SL32 4R023 UL 4.0 23.0 200 31.0 6.3 570-1063-ND 995-SL32-4R023 72J6847
SL05 4R003 4.0 3.0 5 6.0 3.5 570-1085-ND 995-SL05-4R003 72J6676
SL15 4R008 UL 4.0 8.0 40 16.0 5.0 995-SL15-4R008 72J6790
SL10 4R004 UL CSA 4.0 4.0 20 10.0 5.0 570-1125-ND 995-SL10-4R004
SL08 4R003 UL 4.0 3.0 10 8.0 4.0 995-SL08-4R003
SL22 5R006 5.0 6.0 50 22.0 5.5 570-1052-ND 995-SL22-5R006 72J6835
SL22 5R012 UL CSA 5.0 12.0 100 22.0 6.0 570-1053-ND 995-SL22-5R012 72J6836
SL32 5R020 UL CSA 5.0 20.0 200 31.0 6.0 570-1064-ND 995-SL32-5R020 72J6848
SL18 5R006 5.0 6.0 75 19.0 6.0 570-1067-ND 995-SL18-5R006 72J6812
SL12 5R002 5.0 2.0 25 13.0 5.0 72J6754
SL05 5R001 5.0 1.0 5 6.0 3.5 570-1084-ND 995-SL05-5R001 72J6679
MS32 5R020 UL 5.0 20.0 300 31.0 7.0 570-1021-ND 995-MS32-5R020 72J6625
SL10 5R004 5.0 4.0 20 10.0 4.5 72J6726
AS32 5R020 5.0 20.0 300 32.0 8.4 570-1106-ND 995-AS32-5R020
AS35 5R025 5.0 25.0 600 36.0 8.5 570-1114-ND
SL12 5R004 UL 5.0 4.0 40 12.0 5.0 570-1134-ND 995-SL12-5R004 72J6756
SL08 5R002 UL 5.0 2.0 10 8.0 4.0 570-1121-ND 995-SL08-5R002
SL10 5R003 UL 5.0 3.0 20 10.0 4.0 995-SL10-5R003
MS35 5R025 5.0 25.0 600 38.0 10.0 570-1029-ND 995-MS35-5R025
SL08 5R003 CSA 5.0 3.0 10 8.0 4.0 995-SL08-5R003
SL15 5R006 UL 5.0 6.0 50 15.0 4.5 995-SL15-5R006
SL22 7R010 UL CSA 7.0 10.0 100 22.0 6.0 570-1055-ND 995-SL22-7R010 72J6839
SL18 7R005 7.0 5.0 75 19.0 6.0 72J6813
SL15 7R005 UL 7.0 5.0 60 16.0 6.0 995-SL15-7R005 72J6803
MS32 7R015 UL 7.0 15.0 250 31.0 10.0 570-1022-ND 995-MS32-7R015 72J6627
SL15 7R005 7.0 5.0 60 15.0 4.5 995-SL15-7R005 72J6803
SL15 5R007 UL CSA 7.0 5.0 50 15.5 5.0 570-1070-ND 995-SL15-5R007
SL08 7R002 CSA 7.0 2.0 8 8.0 2.8 995-SL08-7R002
SL12 8R004 8.0 2.0 25 13.0 6.0 72J6761
SL12 8R003 UL 8.0 3.0 25 12.0 5.0 570-1130-ND 995-SL12-8R003
SL22 10005 10.0 5.0 90 22.0 5.0 570-1032-ND 995-SL22-10005 72J6817
SL22 10007 UL 10.0 7.0 90 22.0 5.0 570-1033-ND 995-SL22-10007 72J6818
SL22 10008 UL CSA 10.0 8.0 90 22.0 6.0 570-1034-ND 995-SL22-10008 72J6819
SL32 10015 UL CSA 10.0 15.0 150 31.0 6.0 570-1058-ND 995-SL32-10015 72J6844
SL18 10005 10.0 5.0 75 19.0 6.0 570-1068-ND 995-SL18-10005 72J6808
SL12 10006 UL 10.0 6.0 40 13.0 5.5 570-1078-ND 995-SL12-10006 72J6734
SL12 10004 10.0 4.0 40 13.0 5.5 570-1079-ND 995-SL12-10004 72J6732
SL10 10003 UL CSA 10.0 3.0 17 10.0 5.0 570-1082-ND 995-SL10-10003 72J6711
SL03 10001 10.0 1.0 2 3.0 3.0 570-1088-ND 995-SL03-10001 72J6655
MS22 10008 UL 10.0 8.0 200 23.0 9.5 570-1003-ND 995-MS22-10008 72J6608
MS32 10015 UL 10.0 15.0 250 31.0 9.3 570-1014-ND 995-MS32-10015 72J6620
MS35 10018 10.0 18.0 500 37.0 11.0 570-1024-ND 995-MS35-10018 72J6630
SL10 10004 CSA 10.0 4.0 17 10.0 4.5 995-SL10-10004 72J6712
SL15 10006 UL CSA 10.0 6.0 55 16.0 5.5 995-SL15-10006 72J6769
SL22 10009 10.0 9.0 100 22.0 5.0 570-1035-ND 995-SL22-10009-B 72J6820
SL10 10002 10.0 2.0 10 10.0 4.5 995-SL10-10002 72J6710
SL12 10006-03 10.0 6.0 40 13.0 6.0 SL12 10006-03-ND 995-SL12-10006-03
AS32 10015 UL 10.0 15.0 250 30.0 8.5 570-1107-ND 995-AS32-10015
AS35 10018 10.0 18.0 500 36.0 8.5 570-1115-ND 995-AS35-10018
SL08 10002 UL CSA 10.0 2.0 10 8.0 5.0 570-1094-ND 995-SL08-10002 72J6684
SL12 10005 UL CSA 10.0 5.0 60 12.0 5.1 570-1131-ND 995-SL12-10005
SL22 14005 14.0 5.0 75 22.0 5.0 570-1038-ND 995-SL22-14005 72J6823
SL22 14007 UL CSA 14.0 7.0 75 22.0 6.0 570-1039-ND 995-SL22-14007 72J6824
MS32 15012 UL 15.0 12.0 250 31.0 10.0 570-1015-ND 995-MS32-15012 72J6621
SL12 15004 UL 15.0 4.0 40 12.0 5.0 570-1132-ND 995-SL12-15004
SL22 16004 UL CSA 16.0 4.0 100 22.0 7.0 570-1040-ND 995-SL22-16004 72J6825
SL18 16004 16.0 4.0 75 19.0 6.0 72J6809
SL15 16004 UL CSA 16.0 4.4 50 15.0 4.5 995-SL15-16004
SL22 16005 UL 16.0 5.0 1 995-SL22-16005
SL12 17004 UL 17.5 4.0 30 11.5 5.1 995-SL12-17004
SL22 20005 UL CSA 20.0 5.0 125 22.0 7.0 SL22 20005-ND 995-SL22-20005 26K6064
SL22 20007 20.0 7.0 125 22.0 5.0 570-1042-ND 995-SL22-20007 72J6830
SL12 20003 UL 20.0 3.0 35 13.0 5.5 570-1076-ND 995-SL12-20003 72J6748
MS22 20005 UL 20.0 5.0 180 20.0 9.0 570-1007-ND 995-MS22-20005 72J6612
MS32 20008 UL 20.0 8.0 250 31.0 10.0 570-1017-ND 995-MS32-20008 72J6623
MS32 20010 UL 20.0 10.0 250 31.0 10.0 570-1018-ND 995-MS32-20010 72J6624
MS35 20010 20.0 10.0 500 37.0 11.0 570-1026-ND 995-MS35-20010 72J6632
SL08 20002 20.0 2.0 8 9.0 4.3 570-1083-ND 995-SL08-20002 72J6693
AS32 20010 20.0 10.0 250 29.0 9.0 570-1108-ND 995-AS32-20010
AS35 20010 20.0 10.0 500 36.0 9.0 570-1116-ND 995-AS35-20010
SL12 25002 25.0 2.0 30 13.0 5.5 570-1075-ND 995-SL12-25002 72J6750
SL15 25003 CSA 25.0 3.0 50 16.0 6.0 995-SL15-25003 72J6785
SL12 25003 UL 25.0 3.0 45 12.0 5.1 570-1127-ND 995-SL12-25003 72J6751
SL10 25002 UL 25.0 2.0 20 10.0 5.0 570-1123-ND 995-SL10-25002
SL15 25004 UL 25.0 4.0 50 15.0 4.5 995-SL15-25004
SL22 30005 UL CSA 30.0 5.0 80 22.0 6.0 570-1048-ND 995-SL22-30005 72J6832
SL05 30001 30.0 1.0 3 6.0 2.7 570-1086-ND 995-SL05-30001 72J6673
MS15 30004 UL 30.0 4.2 135 17.0 9.0 570-1001-ND 995-MS15-30004 72J6606
MS22 30005 UL 30.0 5.0 150 23.0 9.0 570-1009-ND 995-MS22-30005 72J6614
SL18 30006 30.0 6.0 65 18.0 6.5 570-1100-ND 995-SL18-30006
SL15 30004 UL 30.0 4.0 40 15.0 5.0 995-SL15-30004
SL08 33001 UL 33.0 1.3 8 8.0 4.0 570-1095-ND 995-SL08-33001 72J6697
SL22 40005 40.0 5.0 63 22.0 5.0 570-1049-ND 995-SL22-40005 72J6834
MS15 40004 UL 40.0 4.1 135 17.0 8.0 570-1002-ND 995-MS15-40004 72J6607
SL15 40004 UL 40.0 4.0 35 15.0 5.0 570-1136-ND 995-SL15-40004 72J6791
SL12 40002 UL 40.0 2.0 20 12.0 5.0 570-1128-ND 995-SL12-40002
SL10 40002 UL 40.0 2.0 15 11.0 6.0 570-1124-ND 995-SL10-40002
SL22 47003 47.0 3.0 90 22.0 5.0 42M9891
SL15 47003 47.0 3.0 50 16.0 6.0 570-1071-ND 995-SL15-47003 72J6792
SL18 47003 47.0 3.0 75 19.0 7.5 570-1101-ND 995-SL18-47003 72J6811
SL22 50004 UL CSA 50.0 4.0 80 22.0 7.0 570-1051-ND 995-SL22-50004 72J6837
SL10 50002 50.0 2.0 18 10.0 4.0 570-1080-ND 995-SL10-50002 72J6728
MS22 50004 UL 50.0 4.0 240 23.0 10.0 570-1010-ND 995-MS22-50004 72J6615
MS32 50006-L UL 50.0 6.0 250 31.0 7.0 995-MS32-50006-L 72J6626
SL12 50002 UL 50.0 2.0 20 13.0 5.0 570-1074-ND 995-SL12-50002 72J6758
AS32 50006 50.0 6.0 250 30.0 9.0 570-1109-ND 995-AS32-50006
SL08 50001 UL 50.0 1.1 12 8.0 4.0 570-1096-ND 995-SL08-50001 72J6705
SL10 50001 UL 50.0 1.1 18 10.0 5.0 570-1126-ND 995-SL10-50001
MS32 50006 50.0 6.0 250 30.0 7.0 570-1020-ND 995-MS32-50006
SL22 60003 UL CSA 60.0 3.0 72 22.0 7.0 570-1054-ND 995-SL22-60003 72J6838
SL15 60002 UL 60.0 2.0 50 16.0 6.0 570-1069-ND 995-SL15-60002 72J6800
SL15 60004 60.0 4.0 50 16.0 6.0 570-1137-ND 995-SL15-60004 72J6801
MS22 75004 UL 75.0 4.0 240 23.0 9.0 570-1011-ND 995-MS22-75004 72J6616
SL12 80002 UL 80.0 2.0 30 13.0 6.0 570-1129-ND 995-SL12-80002 72J6762
SL15 80002 UL 80.0 2.0 45 15.0 5.5 570-1138-ND 995-SL15-80002
SL22 12102 120.0 2.0 80 22.0 6.0 570-1036-ND 995-SL22-12102 72J6821
SL22 12103 UL CSA 120.0 3.0 80 22.0 6.0 570-1037-ND 995-SL22-12103 72J6822
MS22 12102 UL 120.0 2.0 220 23.0 10.0 570-1004-ND 995-MS22-12102 72J6609
MS22 12103 UL 120.0 3.0 220 23.0 10.0 570-1005-ND 995-MS22-12103 72J6610
MS22 12104 UL 120.0 4.0 220 23.0 10.0 570-1006-ND 995-MS22-12104 72J6611
SL08 12101 UL 120.0 1.0 10 8.0 4.0 570-1097-ND 995-SL08-12101 72J6688
SL12 12103 120.0 3.0 25 12.0 5.0 72J6738
SL05 12101 120.0 1.0 12 5.5 2.7 995-SL05 12101 72J6669
SL15 12102 UL 120.0 2.0 40 15.0 5.5 570-1135-ND 995-SL15-12102
SL10 12101 UL 120.0 1.0 14 10.5 5.0 570-1122-ND 995-SL10-12101
SL12 12101 CSA 120.0 1.0 25 12.0 5.0 995-SL12-12101
SL12 12102 UL 120.0 2.0 25 12.0 5.0 995-SL12-12102
MS12 15102 UL 150.0 2.0 110 13.5 8.7 570-1000-ND 995-MS12-15102 72J6605
SL12 15102 UL 150.0 2.0 10 995-SL12-15102
SL22 22101 220.0 1.0 2 3.0 3.0 570-1043-ND 995-SL22-22102 72J6831
SL15 22102 UL CSA 220.0 2.0 40 16.0 6.0 570-1073-ND 995-SL15-22102 72J6784
SL03 22102 220.0 2.0 2 3.0 3.0 570-1087-ND 995-SL03-22101 72J6671
MS22 22103 UL 220.0 3.5 75 23.0 10.0 570-1008-ND 995-MS22-22103 72J6613
SL12 22101 UL 220.0 1.0 30 12.0 5.5 570-1133-ND 995-SL12-22101
SL22 22102 220.0 2.0 72 22.0 5.5 995-SL22-22102

For this example, we recommend using the SL03 12101 thermistor because it meets all the necessary requirements for this application.

Contact Us! 

Do you have questions? Feel free to contact us for help choosing the right thermistor. Our thermistors are also available at Digi-Key, Mouser, and FarnellThanks for reading!


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