electronics- voltage dividersdenethor.wlu.ca/pc320/lectures/vdivbeam.pdf · voltage divider (no...

Voltage dividersVariable resistors

Specific voltage dividers

ElectronicsVoltage Dividers

Terry Sturtevant

Wilfrid Laurier University

May 31, 2017

Terry Sturtevant Electronics Voltage Dividers

Specific voltage dividersVoltage divider (no load)Voltage divider (with load RL )

Applications of Kirchhoff’s Voltage Law

Voltage dividers

Applications of Kirchhoff’s Voltage Law

Voltage dividers

Vs = VR1 + VR2

A voltage divider “divides” the supply voltage

A voltage divider “divides” the supply voltageIt’s useful when you need a different voltage than the supply

Part of Vs across R1

VR2 = Vs − VR1

Since the current is the same in both resistors, the voltage isdivided between the two; thus it is a voltage divider.

Voltage divider circuits are very common, even when one orboth circuit elements aren’t resistors.

Since the current is the same in both resistors, the voltage isdivided between the two; thus it is a voltage divider.Voltage divider circuits are very common, even when one orboth circuit elements aren’t resistors.

Usually a voltage divider is drawn like this so it looks like aladder.

Usually a voltage divider is drawn like this so it looks like aladder.As you climb the ladder, the voltage increases.

Since I1 = I2,

Since I1 = I2, (by Kirchhoff’s current law,)

Since I1 = I2, (by Kirchhoff’s current law),and Vs = VR1 + VR2 ,

Since I1 = I2, (by Kirchhoff’s current law),and Vs = VR1 + VR2 ,(by Kirchhoff’s voltage law),

Since I1 = I2, (by Kirchhoff’s current law),and Vs = VR1 + VR2 ,(by Kirchhoff’s voltage law),so Vs = I1R1 + I1R2

Since I1 = I2, (by Kirchhoff’s current law),and Vs = VR1 + VR2 ,(by Kirchhoff’s voltage law),so Vs = I1R1 + I1R2 = I (R1 + R2)

Since I1 = I2, (by Kirchhoff’s current law),and Vs = VR1 + VR2 ,(by Kirchhoff’s voltage law),so Vs = I1R1 + I1R2 = I (R1 + R2)I = Vs

So Vout = V2 = IR2

So Vout = V2 = IR2 = VsR1+R2

R2R1+R2

If R1 gets smaller, thenVout = Vs

)gets bigger.

Vout = Vs(

R2R1+R2

If R1 gets bigger, thenVout = Vs

)gets smaller.

Voltage divider (no load)

If R1 = 5Ω , R2 = 10Ω, Vs = 5VVout

R2R1+R2

)= 3.3V

If R1 = 5Ω , R2 = 10Ω, Vs = 5V

R2R1+R2

)= 3.3V

If R1 = 5Ω , R2 = 10Ω, Vs = 5VVout

R2R1+R2

)= 3.3V

If R1 = 5Ω , R2 = 10Ω, Vs = 5VVout

R2R1+R2

= 3.3V

If R1 = 5Ω , R2 = 10Ω, Vs = 5VVout

R2R1+R2

)= 3.3V

Voltage divider (with load RL )

Load will reduce the output voltage

R2 RL?

Some current goes through R2, but some goes through RL so theeffective value of R2 is reduced.

If R1 = 5Ω , R2 = 10Ω, Vs = 5V and RL = 10Ω

Parallel resistance of R2 and RL = R2RLR2+RL

= 10×1010+10 = 5Ω

Thus Vout

= VsRp

R1+Rp= 5

)= 2.5V

If R1 = 5Ω , R2 = 10Ω, Vs = 5V and RL = 10ΩParallel resistance of R2 and RL = R2RL

= 10×1010+10 = 5Ω

Thus Vout

= VsRp

R1+Rp= 5

)= 2.5V

= 10×1010+10 = 5Ω

Thus Vout

= VsRp

R1+Rp= 5

)= 2.5V

= 10×1010+10 = 5Ω

Thus Vout

= VsRp

R1+Rp= 5

)= 2.5V

= 10×1010+10 = 5Ω

Thus Vout

= VsRp

R1+Rp= 5

= 2.5V

= 10×1010+10 = 5Ω

Thus Vout

= VsRp

R1+Rp= 5

)= 2.5V

Variable resistors

Often it is useful to have variable resistors in a circuit.These are sometimes called potentiometers or trimmers.

Variable resistors

Often it is useful to have variable resistors in a circuit.

These are sometimes called potentiometers or trimmers.

Variable resistors

Often it is useful to have variable resistors in a circuit.These are sometimes called potentiometers or trimmers.

Vout = Vin(

R2R1+R2

True if Iout ≡ 0

R1 + R2 = a constant.

Here is a trimmer.

Here is a trimmer. The top line should look familiar.

The potentiometer has three pins.

The resistance given is between the two end pins.The third pin is called the wiper.A small screwdriver can be used to move the wiper from oneend to the other, or anywhere in between.The resistance between the two end pins will be constant.If you want a resistance which varies, just use the wiper andone end pin.

The potentiometer has three pins.The resistance given is between the two end pins.

The third pin is called the wiper.A small screwdriver can be used to move the wiper from oneend to the other, or anywhere in between.The resistance between the two end pins will be constant.If you want a resistance which varies, just use the wiper andone end pin.

The potentiometer has three pins.The resistance given is between the two end pins.The third pin is called the wiper.

A small screwdriver can be used to move the wiper from oneend to the other, or anywhere in between.The resistance between the two end pins will be constant.If you want a resistance which varies, just use the wiper andone end pin.

The potentiometer has three pins.The resistance given is between the two end pins.The third pin is called the wiper.A small screwdriver can be used to move the wiper from oneend to the other, or anywhere in between.

The resistance between the two end pins will be constant.If you want a resistance which varies, just use the wiper andone end pin.

The potentiometer has three pins.The resistance given is between the two end pins.The third pin is called the wiper.A small screwdriver can be used to move the wiper from oneend to the other, or anywhere in between.The resistance between the two end pins will be constant.

If you want a resistance which varies, just use the wiper andone end pin.

The potentiometer has three pins.The resistance given is between the two end pins.The third pin is called the wiper.A small screwdriver can be used to move the wiper from oneend to the other, or anywhere in between.The resistance between the two end pins will be constant.If you want a resistance which varies, just use the wiper andone end pin.

Here’s a different view.

Here’s a different view. The wiper is in the middle.

From the top, this one has 10 dashes to represent intervals of roughlyR/10.

This is a slightly different style.

This is a slightly different style. Note the graphical indication of thewiper.

The potentiometer can be used for a variable voltage divider.

Connect the two ends of your supply to the two end pins.Measure the output voltage on the wiper.Adjusting the wiper will change the output voltage from oneend of the supply to the other, or to anywhere in between.

The potentiometer can be used for a variable voltage divider.Connect the two ends of your supply to the two end pins.

Measure the output voltage on the wiper.Adjusting the wiper will change the output voltage from oneend of the supply to the other, or to anywhere in between.

The potentiometer can be used for a variable voltage divider.Connect the two ends of your supply to the two end pins.Measure the output voltage on the wiper.

Adjusting the wiper will change the output voltage from oneend of the supply to the other, or to anywhere in between.

The potentiometer can be used for a variable voltage divider.Connect the two ends of your supply to the two end pins.Measure the output voltage on the wiper.Adjusting the wiper will change the output voltage from oneend of the supply to the other, or to anywhere in between.

Specific voltage dividersSwitches in voltage dividersResistive sensors in voltage dividers

Switches in voltage dividers

One of the simplest forms of voltage divider is where one ofthe elements is a switch.A switch can be thought of as a resistor which can have avalue of either zero or infinity.Following is an illustration of a voltage divider where oneelement is a switch.

One of the simplest forms of voltage divider is where one ofthe elements is a switch.

A switch can be thought of as a resistor which can have avalue of either zero or infinity.Following is an illustration of a voltage divider where oneelement is a switch.

One of the simplest forms of voltage divider is where one ofthe elements is a switch.A switch can be thought of as a resistor which can have avalue of either zero or infinity.

Following is an illustration of a voltage divider where oneelement is a switch.

One of the simplest forms of voltage divider is where one ofthe elements is a switch.A switch can be thought of as a resistor which can have avalue of either zero or infinity.Following is an illustration of a voltage divider where oneelement is a switch.

Vout = Vin(

R2R1+R2

True if Iout ≡ 0

Vout = Vin(

R2R1+R2

True if Iout ≡ 0

R1 R1 = 0⇒ V1 = 0

V2 = Vout = Vin

R1 R1 =∞⇒ I = 0

V2 = Vout = 0

R1 R1 = 0⇒ V1 = 0

V2 = Vout = Vin

R1 R1 =∞⇒ I = 0

V2 = Vout = 0

So if one of the elements is a switch, the output variesbetween 0 and Vin.

If either resistor in a voltage divider is variable, then a rangeof output voltages is possible.

So if one of the elements is a switch, the output variesbetween 0 and Vin.If either resistor in a voltage divider is variable, then a rangeof output voltages is possible.

Resistive sensors in voltage dividers

Vout = Vin(

R2R1+R2

True if Iout ≡ 0

If we want to put a variable resistor in a voltage divider, thenwe need to choose the other resistor.

To make the output vary over as large a range as possible asthe variable resistor goes from Rmin to Rmax , it turns out wewant to choose the other resistor, R so thatR =

√Rmin × Rmax

If we want to put a variable resistor in a voltage divider, thenwe need to choose the other resistor.To make the output vary over as large a range as possible asthe variable resistor goes from Rmin to Rmax , it turns out wewant to choose the other resistor, R so that

R =√

Rmin × Rmax

If we want to put a variable resistor in a voltage divider, thenwe need to choose the other resistor.To make the output vary over as large a range as possible asthe variable resistor goes from Rmin to Rmax , it turns out wewant to choose the other resistor, R so thatR =

√Rmin × Rmax

electronics- voltage dividersdenethor.wlu.ca/pc320/lectures/vdivbeam.pdf · voltage divider (no...

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