Need clarification on dot convention for magnetically couped circuits

[kevinf]

i have started to use dot convention for magnetically circuit. my understanding is that if the currents for primary winding and current in the secondary winding are clockwise and the dots are ontop of the inductors then the mutual inductance value would be negative because the secondary winding current would be coming out of the dot rather then going in.

when both currents are going clockwise and the dot in the primary winding is on the top and the dot for the secondary winding is on the bottom then the mutual inductance values for the two current would be positive since both currents are going into the dot. but sometimes i see other places use different ways. can you guys help me understand the convention or provide me with what you do to understand the circuit?

thanks

 

[berkeman]

i have started to use dot convention for magnetically circuit. my understanding is that if the currents for primary winding and current in the secondary winding are clockwise and the dots are ontop of the inductors then the mutual inductance value would be negative because the secondary winding current would be coming out of the dot rather then going in.

when both currents are going clockwise and the dot in the primary winding is on the top and the dot for the secondary winding is on the bottom then the mutual inductance values for the two current would be positive since both currents are going into the dot. but sometimes i see other places use different ways. can you guys help me understand the convention or provide me with what you do to understand the circuit?

thanks

The first way you stated it is correct. I prefer to think in terms of voltages, though, since that is easier for me to remember.

Picture a toroid with two coils wound on it with the same winding direction. Put the dot on the beginning of each winding. When you drive the dot end of the first winding with an AC voltage and there is a load resistor on the 2nd winding, then the phase of the voltage will be the same on the dot ends of both windings.

 

[kevinf]

thanks for your explanation but i don't think i completely understand it because i am more of a visual person. for example in this circuit, the two currents are going clockwise and the dots are on top but the mesh equations +17j*I_2 and +17j I_1, shouldn't they both be negative?

http://yfrog.com/ca91465469p

 

[berkeman]

thanks for your explanation but i don't think i completely understand it because i am more of a visual person. for example in this circuit, the two currents are going clockwise and the dots are on top but the mesh equations +17j*I_2 and +17j I_1, shouldn't they both be negative?

http://yfrog.com/ca91465469p

No, the currents are correct as drawn. The current into the primary corresponds to the positive phase drive voltage, and the corresponding positive phase output voltage causes the output current to flow in phase through the load resistance.

 

[kevinf]

but the current in the secondary is coming out of the dot (like going from negative to positive in a voltage source) rather then going in, doesn't that mean that it is a negative mutual inducatance?

 

[Carl Pugh]

?what happens on a winding that is not connected?
?There is no current, so there is no voltage?

Why make something difficult that is easy.
Forget about current.
When the dot on one winding goes positive, the dot on all the other windings go positive.

 

[Bob S]

I believe the dot convention is directly related to Faraday's Law of induction. An increasing current entering the dotted end of the input winding produces a positive voltage at the dotted end of the output windings.

Bob S

 

[Carl Pugh]

Why make things complicated?

Transformers are inductive, so the current lags the input voltage by 90 degrees.
Does this mean that the output voltage lags the input voltage by 90 degrees?

We both know that in an ordinary single phase transformer, the input voltage and output voltage are nearly in phase. (or 180 degrees out of phase)

For placing polarity dots on transformers, it is easier to forget about current and merely use voltage.

 

[ezcheez]

i have started to use dot convention for magnetically circuit. my understanding is that if the currents for primary winding and current in the secondary winding are clockwise and the dots are ontop of the inductors then the mutual inductance value would be negative because the secondary winding current would be coming out of the dot rather then going in.

The first way you stated it is correct. I prefer to think in terms of voltages, though, since that is easier for me to remember.

If this is true, then dots and voltages aside, kevinf should be correct in his statement that the "17jI1" and "17jI2" referenced later should be "-17jI1" and "-17jI2."

 

[uart]

The equations in the "yfrog" linked cct are wrong. Should be -j17 I2 in the first equation and -j17 I1 in the second.

Reason : v_1 = L_1 \frac{d i_1}{dt} - M \frac{d i_2}{dt} and similarly for secondary.

 

[Antiphon]

Several of the above answers are misunderstandings of both ideal transformers and the dot convention. Faradays law does not apply in the sense of increasing current producing a fixed voltage. That's not true for the ideal transformer, it's true for coupled inductors. The dot convention is on voltage alone. If you connect a 9 volt battery (dc) to the primary of an ideal transformer with the dot on the positive battery terminal and if the ideal transformer is a 2:1 step-up, the secodary dot will be a positive 18 volts DC. Yes, I mean DC. That's what an ideal transformer means. It has zero inductance as well.

 

[ezcheez]

Antiphon:

If an ideal transformer has zero inductance, then what is the mechanism causing the transformation, and do such transformers exist?

 

[NexusN]

I am not sure if I have understood the dot convention correctly,
but my idea is based on the tendency of the inductor refusing to change the current(magnetic flux inside it to be more accurate).

Take a look at this picture:

At the very beginning when the switching is open(in OFF mode), no current flowing in neither primary and secondary.

Consider only the primary side,
when we close the switch(turn to ON mode), current starts flowing clock-wise in primary, that is, current flows into the dot.
And that the inductor shows a tendency to keep the current(zero current), that is, tries to push the current out of the dot creating a backward current flow tendency.

The same idea applied on the secondary side, the inductor(the transformer one) on the secondary side presented the same tendency as primary side transformer inductor did, pushing current out of the dot, eventually causing a clock-wise current flow on secondary side.

For an opposite case, consider the same circuit but at a steady state that clock-wise current has flown in the two sides for some time, that is, during the ON state(when the switch is close), we suddenly open the switch.

No doubt the current flow in the primary side is cut(neglecting leakage inductance and assume perfect coupling), the transformer inductors then present a tendency of current flow, that is, to keep the current flowing clockwise in primary side, which means the primary side transformer inductor tries to push current into the dot, and therefore the secondary side transformer inductor too, the secondary inductor tries to present a anti-clockwise current flow at this time. That is also the reason an extra diode is added at the right of the transformer output at the secondary side to prevent such anti-clockwise current flow from happening.

Eventually we have a "buck" converter with galvanic isolation.

This is for your reference, I am not sure the correctness of my speech and in case you found any errors, please feel free to tell me.

 

[Skaperen]

This is an old thread so I don't know if it will get as wide a reading now. Maybe start a new one?

My understand of the dot convention is based on construction. If you were to bundle all the wires together, for example by using a multi conductor cable, and wind the cable/bundle around the core (or air as the case may be), all the windings will have a dot at one end of the cable, at the same end.

The effect is that you would get the same voltage polarity coming out one winding at the dot as going in the other winding at the dot. But the current would be going through those windings in opposite direction, almost canceling each other out. This is how a transformer or other inductively coupled circuit works. Whatever field that is present from the primary winding that gets coupled to the secondary is "trying" to reduce the field by inducing a current in the opposite direction ... in both the primary and secondary. In the primary, that limits the current. In the secondary, current will flow when the secondary has a place for it to go. Once that current flows, the field from the secondary cancels out some of the field in the primary (depending on how tightly coupled). Now with the field reduced in the primary, more primary current can flow to make up for the outflow from the secondary. With more primary current, the field maintains an equilibrium over a wide range of power.

 

[Antiphon]

Antiphon:

If an ideal transformer has zero inductance, then what is the mechanism causing the transformation, and do such transformers exist?

I apologize for taking a year to answer your question. I sometimes loose track of threads.

The ideal transformer does not exist. But it is essential for solving circuit problems and understanding real transformers without using field theory.

A real transformer can be modeled as an inductor placed in shunt across the terminals of an ideal transformer.

This construction will not pass DC power any longer.