# How to calculate capacitor value for “stepper motor”

#### xchcui

Joined May 12, 2014
192

Hi.

There are several video clips in youtube that show how to run a stepper motor with a capacitor. Here is one of the video:
Of course,in that way the stepper motor doesn't act as a stepper motor,but it shows how to make it spin without a driver. In the video they use 4 wire(2 coils)stepper motor and made the connection as you can see on my attached circuit diagram,but they didn't explains how to calculate the right value(capacitance)of the capacitor according to the stepper motor specification in order to get a smooth spin and avoiding of burnning the coil.So,how can i calculate(formula)the right value of a capacitor for a stepper motor based on my attached diagram? For example:12v/30mA stepper motor,each coil is 410 ohm.
Thanks.

Last edited:

Joined Jul 18, 2013
22,043
Slo-Syn manual on a stepper motor ran as an AC synchronous motor shows a resistor required in series with the cap.
The required value should result in a phase shift of 90° between the winding pair.
For unknown motors, they recommend using a resistor & capacitor substitution boxes in order to achieve max. torque, minimum vibration, until optimum operation is achieved,
With anything less than optimum will result in random direction and a tendency to reverse at the slightest load change.
For their motors intended for AC synchronism, they publish the values.
BTW, the resistor/capacitor should be in series with the shifted winding.NOT parallel
Max.

#### xchcui

Joined May 12, 2014
192
I am familiar with air conditioners and refrigerators motors,so,as
you mentioned,i know that the secondary coil should be in series with
the run capacitor and in parallel to the main coil(contrary to the attached diagram).So,you probably right in your reply,but the video shows a circuit as i attached and i would like to focus on that specific one.
I just would like to know how to determine the value of the capacitor for such kind of circuit.I know how to make a calculation for a run capacitor,but this circuit is different,so i would like to know what is the formula to find the right capacitance for the attached diagram.
Thanks.

#### shortbus

Joined Sep 30, 2009
8,197
There is no real formula. Like Max said you need to experiment if your not using a Slo-Syn motor that was covered in the Slo-syn manual. A stepper running like this is not very powerful, it's more of a demonstration than something useful.

Joined Jul 18, 2013
22,043
Slo-syn make motor for 120vac/230vac that are constructed virtually the same way as the stepper versions, but for synchronous to the supply
They have the feature on instant stop/start features, (within 1.5 cycles).
Normally 72 rpm on 60Hz.
As mentioned, it is a case of empirical testing if using a motor not specifically designed for this purpose.
As per the Slo-Syn manual advice.
Max.

#### xchcui

Joined May 12, 2014
192
There is no real formula. Like Max said you need to experiment...
I am not agree with that.
When an engineer plan a circuit,first,he chooses all components value according to calculations that he makes.After that,he test the circuit and fix what he needs to fix/change.You can't just take 100 capacitors and test each one with the circuit.
I gave you a simple diagram with just 2 coils,a capacitor and 12vac source,
Do you want to say,that it is impossible to calculate the capacitor value that will make the rotor spin?at least the the value that i can start with?

Joined Jul 18, 2013
22,043
The manufacturere, SloSyn has been making stepper motors for Many decades, and if that is what they suggest (empirical testing) , who am I to argue?
I am repeating what their manual suggests.
The capacitor is in series with the second coil, just the way a 1ph induction motor is.
The capacitor value necessary should produce close to a 90° phase shift.
Alternately, measure the inductive reactance at 50hz/60hz and chose a capacitor to produce the 90°.
Max.

#### shortbus

Joined Sep 30, 2009
8,197
When an engineer plan a circuit,first,he chooses all components value according to calculations that he makes.After that,he test the circuit and fix what he needs to fix/change.You can't just take 100 capacitors and test each one with the circuit.
But you can do it by testing a few with a range between them. You find what is close, then you test within that range, to find the best fit. Like what Max said in his first post you use a capacitor/resistor substitution box https://www.nutsvolts.com/magazine/article/September2016_Capacitor-Resistor-Substitution-Boxes
Something that was used before computer modeling of circuits.

Do you want to say,that it is impossible to calculate the capacitor value that will make the rotor spin?at least the the value that i can start with?
Max answered this in post #7 -
Alternately, measure the inductive reactance at 50hz/60hz and chose a capacitor to produce the 90°.
Max.
Nothing like this is impossible, it just takes some thought and common knowledge. And experimentation since your doing something that isn't very well documented.

#### Danko

Joined Nov 22, 2017
1,023
For example - without additional resistor we can not have
simultaneously equal currents in coils and phase shift exactly 90°.
But it still works.

The same, but with resistor:

So,how can i calculate(formula)the right value of a capacitor for a stepper motor based on my attached diagram? For example:12v/30mA stepper motor,each coil is 410 ohm.
Unfortunately, it is impossible to simulate your motor, because you did not tell us inductance value of coils.

Last edited:

Joined Jul 18, 2013
22,043
For example - without additional resistor we can not have
simultaneously equal currents in coils and phase shift exactly 90°.
But it still works.
Except it is not wired that way one winding is across supply the other winding in series with cap, across the supply.
Max.

#### xchcui

Joined May 12, 2014
192
Unfortunately, it is impossible to simulate your motor, because you did not tell us inductance value of coils.
The phase inductance is 130mH.
Btw,the person in the video(and also on other videos)used a polarized capacitor rather than non-polar ones.Did they choose the polarised cap on purpose or i can use also the non-polar cap?

#### Danko

Joined Nov 22, 2017
1,023
The phase inductance is 130mH.
For this inductance and R_coil=410 Ω, capacitor should be 60 uF,
then phase shift is 90°, but currents in coils are too different:

This problem solved in more complicated circuit:
(Because coils are connected in series, voltage source is 24 VAC, 50 Hz)

You can simulate circuits yourself in free LTspice software:

Did they choose the polarised cap on purpose or i can use also the non-polar cap?
Capacitors must be non-polarized.
So,how can i calculate(formula)the right value of a capacitor for a stepper motor based on my attached diagram?
Easy. It is possible, if R_L=X_L or R_L<X_L.
For stepper motor or split phase induction motor:
R_L=X_L (if R_L<X_L, then connect additional resistor in series with C);
X_C=2*X_L (if C connected in series with L);
X_C=X_L (if C connected in parallel to L).
REACTANCE CALCULATOR
Still does not look right, compared to the SloSyn example motors.
Max.
@xchcui, below is highly recommended by @MaxHeadRoom
"looks right, compared to the SloSyn" circuit, where 0.75 uF capacitor
provided accurate 90° phase shift.

You may not use R1 at all, because any resistance decreases current of L2.

#### Attachments

• 1.3 KB Views: 4
Last edited:

Joined Jul 18, 2013
22,043
Still does not look right, compared to the SloSyn example motors.
Max.

#### Attachments

• 1.9 MB Views: 11

#### xchcui

Joined May 12, 2014
192
@xchcui, below is highly recommended by @MaxHeadRoom
"looks right, compared to the SloSyn" circuit, where 0.65 uF capacitor
provided accurate 90° phase shift.
You may not use R1 at all, because any resistance decreases current of L2.

So,do you mean,that i should build the circuit as we can see a bove:
while L1 is in parallel with L2 which is in series with a non-polar capacitor(650 nano farad),but without the resistor(R1)that is shown in your last diagram?
The source of this circuit,while you made the simulation is 12VAC 50Hz,
right?
Can we trust on the capacitor value(650nF)that LTspice software simulation gave us?What is the range value of capacitors that should i buy in order to cover and fix a possibility that the capacitor value(650nF)is wrong?

#### Danko

Joined Nov 22, 2017
1,023
So,do you mean,that i should build the circuit as we can see a bove:
while L1 is in parallel with L2 which is in series with a non-polar capacitor(650 nano farad),but without the resistor(R1)that is shown in your last diagram?
I did not say "you should build this circuit".
The source of this circuit,while you made the simulation is 12VAC 50Hz,
right?
Right.
Can we trust on the capacitor value(650nF)that LTspice software simulation gave us?What is the range value of capacitors that should i buy in order to cover and fix a possibility that the capacitor value(650nF)is wrong?
LTspice did not take into account some electrical and electromechanical parameters of motor, so circuit may need to be tuned with help of oscilloscope.

Information, I provided you, is enough to make some important conclusions:
A. Ratio R_L/X_L should be ≤1. In your motor it is 410Ω/40.841Ω=10.04, so this motor can not work from AC with full mechanical power, using parallel or series capacitor.
B. As shown on picture, in circuit with capacitor 60uF, connected in parallel to coil, current in L2 is 10 times lower than current in L1, so mechanical power will 1% from nominal.
C. On this diagram, in circuit with capacitor 0.75uF, connected in series with coil, current in L2 is 10 times lower than current in L1, so mechanical power will 1% from nominal.
D. In especially designed for this case circuit, amplitudes of current in coils L1 and L2 are equal, so motor will work with full (100%) nominal mechanical power.

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#### xchcui

Joined May 12, 2014
192
I did not say "you should build this circuit".
Danko.
Thanks alot for taking your time to help me with my question,but when you said that sentence,it brings me to a problem.
All i need is to make the motor spin for 2 minute with a load(that contains a set of plastic gears)in order to test
them.Thats all.Not to make it spin permanently.
If only one capacitor will do it,it will be great.
I need to make a special purchase of a proper value of capacitor,for this one time/2 minute test and it will be waste of money
and unnecessary to buy several value of capacitors for one time test,while the expert members in this forum,which have the experience with that calculation can give me the proper value and save me all the hassle.
I appreciate your effort and time that you spend in your answer,but unfortunately,i am not sure how to choose the proper capacitor value,especially,when you said that i shouldn't rely on the components value in your diagrams.
Can you give me a proven value that i can buy,as i said,the motor doesn't need to spin perfect,it just need to spin 2 minutes to checked the condition of the load(set of gears).
Thanks.

#### shortbus

Joined Sep 30, 2009
8,197
All i need is to make the motor spin for 2 minute with a load(that contains a set of plastic gears)in order to test
them.Thats all.Not to make it spin permanently.
This begs the question of why your even using this motor? And if you have to use this motor why you aren't just using a stepper motor driver to do it? Just because it's called a "stepper motor" doesn't mean it can't or won't rotate at a set RPM if the driver is used at the correct frequency. A stepper driver is very inexpensive on Ebay or Amazon and is ready to work when you get it.

#### xchcui

Joined May 12, 2014
192
Buy these capacitors and experiment with them:
120pcs 50V 15 Values 1uF - 2200uF Electrolytic Capacitor Assortment Tool Set.
$4.99 for set. Or 120pcs 12 Values 1uF-470uF Assorted Electrolytic Capacitor Assortment Kit Radial. US$2.45 for set.
View attachment 209341
C1 and C2 should have same value.
Couple C1, C2 works as non-polarized capacitor.
So,the two 100uF(+--+) capacitors will work?
Is it the proven value that i need?
or you just gave a capacitance value for an example?
and that is the reason that you marked them with asterisks?

This begs the question of why your even using this motor?
This motor is came together with the set of the plastic gears.
And if you have to use this motor why you aren't just using a stepper motor driver to do it?
Because i don't have a stepper motor driver and i am not going to buy a driver only to test something one time.
Using a 1 or 2 caps for one time test more practical to me and make more sense.If on the way i could learn how to make a simple calculation to determine the value it was better,but apparently and unfortunately,there is not a simple formula for my case.

Joined Jul 18, 2013
22,043
If this is a one time usage just to run the motor, why not do a little empirical testing, until you get it to run smoothly.??
It doesn't sound as though you are putting it into service?
Max.