Transistor Circuits

 

This page explains the operation of transistors in circuits. Practical matters such as testing, precautions when soldering and identifying leads are covered by the Transistors page.

Transistor circuit symbols

 

Types of transistor

There are two types of standard transistors, NPN and PNP, with different circuit symbols. The letters refer to the layers of semiconductor material used to make the transistor. Most transistors used today are NPN because this is the easiest type to make from silicon. This page is mostly about NPN transistors and if you are new to electronics it is best to start by learning how to use these first.

The leads are labelled base (B), collector (C) and emitter(E).
These terms refer to the internal operation of a transistor but they are not much help in understanding how a transistor is used, so just treat them as labels!

A Darlington pair is two transistors connected together to give a very high current gain.

In addition to standard (bipolar junction) transistors, there are field-effect transistors which are usually referred to as FETs. They have different circuit symbols and properties and they are not (yet) covered by this page.

Transistor currents

The diagram shows the two current paths through a transistor. You can build this circuit with two standard 5mm red LEDs and any general purpose low power NPN transistor (BC108, BC182 or BC548 for example).

The small base current controls the larger collector current.

When the switch is closed a small current flows into the base (B) of the transistor. It is just enough to make LED B glow dimly. The transistor amplifies this small current to allow a larger current to flow through from its collector (C) to its emitter (E). This collector current is large enough to make LED C light brightly.

When the switch is open no base current flows, so the transistor switches off the collector current. Both LEDs are off.

A transistor amplifies current and can be used as a switch.

This arrangement where the emitter (E) is in the controlling circuit (base current) and in the controlled circuit (collector current) is called common emitter mode. It is the most widely used arrangement for transistors so it is the one to learn first.

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Functional model of an NPN transistor

The operation of a transistor is difficult to explain and understand in terms of its internal structure. It is more helpful to use this functional model:

• The base-emitter junction behaves like a diode.
• A base current I_B flows only when the voltage V_BE across the base-emitter junction is 0.7V or more.
• The small base current I_B controls the large collector current Ic.
• Ic = h_FE × I_B (unless the transistor is full on and saturated)
  h_FE is the current gain (strictly the DC current gain), a typical value for h_FE is 100 (it has no units because it is a ratio)
• The collector-emitter resistance R_CE is controlled by the base current I_B:
  • I_B = 0   R_CE = infinity   transistor off
  • I_B small   R_CE reduced   transistor partly on
  • I_B increased   R_CE = 0   transistor full on ('saturated')

Additional notes:

• A resistor is often needed in series with the base connection to limit the base current I_B and prevent the transistor being damaged.
• Transistors have a maximum collector current Ic rating.
• The current gain h_FE can vary widely, even for transistors of the same type!
• A transistor that is full on (with R_CE = 0) is said to be 'saturated'.
• When a transistor is saturated the collector-emitter voltage V_CE is reduced to almost 0V.
• When a transistor is saturated the collector current Ic is determined by the supply voltage and the external resistance in the collector circuit, not by the transistor's current gain. As a result the ratio Ic/I_Bfor a saturated transistor is less than the current gain h_FE.
• The emitter current I_E = Ic + I_B, but Ic is much larger than I_B, so roughly I_E = Ic.

There is a table showing technical data for some popular transistors on the transistors page.

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Touch switch circuit

Darlington pair

This is two transistors connected together so that the current amplified by the first is amplified further by the second transistor. The overall current gain is equal to the two individual gains multiplied together:

Darlington pair current gain, h_FE = h_FE1 × h_FE2
(h_FE1 and h_FE2 are the gains of the individual transistors)

This gives the Darlington pair a very high current gain, such as 10000, so that only a tiny base current is required to make the pair switch on.

A Darlington pair behaves like a single transistor with a very high current gain. It has three leads (B, C and E) which are equivalent to the leads of a standard individual transistor. To turn on there must be 0.7V across both the base-emitter junctions which are connected in series inside the Darlington pair, therefore it requires 1.4V to turn on.

Darlington pairs are available as complete packages but you can make up your own from two transistors; TR1 can be a low power type, but normally TR2 will need to be high power. The maximum collector current Ic(max) for the pair is the same as Ic(max) for TR2.

A Darlington pair is sufficiently sensitive to respond to the small current passed by your skin and it can be used to make a touch-switch as shown in the diagram. For this circuit which just lights an LED the two transistors can be any general purpose low power transistors. The 100kresistor protects the transistors if the contacts are linked with a piece of wire.

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Using a transistor as a switch

When a transistor is used as a switch it must be either OFF or fully ON. In the fully ON state the voltage V_CE across the transistor is almost zero and the transistor is said to be saturated because it cannot pass any more collector current Ic. The output device switched by the transistor is usually called the 'load'.

The power developed in a switching transistor is very small:

• In the OFF state: power = Ic × V_CE, but Ic = 0, so the power is zero.
• In the full ON state: power = Ic × V_CE, but V_CE = 0 (almost), so the power is very small.

This means that the transistor should not become hot in use and you do not need to consider its maximum power rating. The important ratings in switching circuits are the maximum collector current Ic(max) and the minimum current gain h_FE(min). The transistor's voltage ratings may be ignored unless you are using a supply voltage of more than about 15V. There is a table showing technical data for some popular transistors on the transistors page.

For information about the operation of a transistor please see the functional model above.

Protection diode

If the load is a motor, relay or solenoid (or any other device with a coil) a diode must be connected across the load to protect the transistor from the brief high voltage produced when the load is switched off. The diagram shows how a protection diode is connected 'backwards' across the load, in this case a relay coil.

Current flowing through a coil creates a magnetic field which collapses suddenly when the current is switched off. The sudden collapse of the magnetic field induces a brief high voltage across the coil which is very likely to damage transistors and ICs. The protection diode allows the induced voltage to drive a brief current through the coil (and diode) so the magnetic field dies away quickly rather than instantly. This prevents the induced voltage becoming high enough to cause damage to transistors and ICs.

When to use a relay

Relays

Photographs © Rapid Electronics

Transistors cannot switch AC or high voltages (such as mains electricity) and they are not usually a good choice for switching large currents (> 5A). In these cases a relay will be needed, but note that a low power transistor may still be needed to switch the current for the relay's coil!

Advantages of relays:

• Relays can switch AC and DC, transistors can only switch DC.
• Relays can switch high voltages, transistors cannot.
• Relays are a better choice for switching large currents (> 5A).
• Relays can switch many contacts at once.

Disadvantages of relays:

• Relays are bulkier than transistors for switching small currents.
• Relays cannot switch rapidly, transistors can switch many times per second.
• Relays use more power due to the current flowing through their coil.
• Relays require more current than many ICs can provide, so a low power transistor may be needed to switch the current for the relay's coil.

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Connecting a transistor to the output from an IC

Most ICs cannot supply large output currents so it may be necessary to use a transistor to switch the larger current required for output devices such as lamps, motors and relays. The 555 timer IC is unusual because it can supply a relatively large current of up to 200mA which is sufficient for some output devices such as low current lamps, buzzers and many relay coils without needing to use a transistor.

A transistor can also be used to enable an IC connected to a low voltage supply (such as 5V) to switch the current for an output device with a separate higher voltage supply (such as 12V). The two power supplies must be linked, normally this is done by linking their 0V connections. In this case you should use an NPN transistor.

A resistor R_B is required to limit the current flowing into the base of the transistor and prevent it being damaged. However, R_B must be sufficiently low to ensure that the transistor is thoroughly saturated to prevent it overheating, this is particularly important if the transistor is switching a large current (> 100mA). A safe rule is to make the base current I_B about five times larger than the value which should just saturate the transistor.

Choosing a suitable NPN transistor

The circuit diagram shows how to connect an NPN transistor, this will switch on the load when the IC output is high. If you need the opposite action, with the load switched on when the IC output is low (0V) please see the circuit for a PNP transistor below.

The procedure below explains how to choose a suitable switching transistor.

NPN transistor switch
(load is on when IC output is high)

Using units in calculations
Remember to use V, A and or
V, mA and k. For more details
please see the Ohm's Law page.

1. The transistor's maximum collector current Ic(max) must be greater than the load current Ic.

   load current Ic = 
   supply voltage Vs

   load resistance R_L

2. The transistor's minimum current gain h_FE(min) must be at least five times the load current Ic divided by the maximum output current from the IC.

   h_FE(min)  >   5 × 
     load current Ic 

   max. IC current

3. Choose a transistor which meets these requirements and make a note of its properties: Ic(max) and h_FE(min).
   There is a table showing technical data for some popular transistors on the transistors page.
4. Calculate an approximate value for the base resistor:

   R_B = 
   Vc × h_FE
      where Vc = IC supply voltage
     (in a simple circuit with one supply this is Vs)

   5 × Ic

   For a simple circuit where the IC and the load share the same power supply (Vc = Vs) you may prefer to use: R_B = 0.2 × R_L × h_FE

   Then choose the nearest standard value for the base resistor.

5. Finally, remember that if the load is a motor or relay coil a protection diode is required.

Example
The output from a 4000 series CMOS IC is required to operate a relay with a 100 coil.
The supply voltage is 6V for both the IC and load. The IC can supply a maximum current of 5mA.

1. Load current = Vs/R_L = 6/100 = 0.06A = 60mA, so transistor must have Ic(max) > 60mA.
2. The maximum current from the IC is 5mA, so transistor must have h_FE(min) > 60 (5 × 60mA/5mA).
3. Choose general purpose low power transistor BC182 with Ic(max) = 100mA and h_FE(min) = 100.
4. R_B = 0.2 × R_L × h_FE = 0.2 × 100 × 100 = 2000. so choose R_B = 1k8 or 2k2.
5. The relay coil requires a protection diode.

PNP transistor switch
(load is on when IC output is low)

Choosing a suitable PNP transistor

The circuit diagram shows how to connect a PNP transistor, this will switch on the load when the IC output is low (0V). If you need the opposite action, with the load switched on when the IC output is high please see the circuit for an NPN transistor above.

The procedure for choosing a suitable PNP transistor is exactly the same as that for an NPN transistor described above.

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Using a transistor switch with sensors

LED lights when the LDR is dark

LED lights when the LDR is bright

The top circuit diagram shows an LDR (light sensor) connected so that the LED lights when the LDR is in darkness. The variable resistor adjusts the brightness at which the transistor switches on and off. Any general purpose low power transistor can be used in this circuit.

The 10k fixed resistor protects the transistor from excessive base current (which will destroy it) when the variable resistor is reduced to zero. To make this circuit switch at a suitable brightness you may need to experiment with different values for the fixed resistor, but it must not be less than 1k.

If the transistor is switching a load with a coil, such as a motor or relay, remember to add a protection diode across the load.

The switching action can be inverted, so the LED lights when the LDR is brightly lit, by swapping the LDR and variable resistor. In this case the fixed resistor can be omitted because the LDR resistance cannot be reduced to zero.

Note that the switching action of this circuit is not particularly good because there will be an intermediate brightness when the transistor will be partly on (not saturated). In this state the transistor is in danger of overheating unless it is switching a small current. There is no problem with the small LED current, but the larger current for a lamp, motor or relay is likely to cause overheating.

Other sensors, such as a thermistor, can be used with this circuit, but they may require a different variable resistor. You can calculate an approximate value for the variable resistor (Rv) by using a multimeter to find the minimum and maximum values of the sensor's resistance (Rmin and Rmax):

Variable resistor, Rv = square root of (Rmin × Rmax)

For example an LDR: Rmin = 100, Rmax = 1M, so Rv = square root of (100 × 1M) = 10k.

You can make a much better switching circuit with sensors connected to a suitable IC (chip). The switching action will be much sharper with no partly on state.

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A transistor inverter (NOT gate)

Inverters (NOT gates) are available on logic ICs but if you only require one inverter it is usually better to use this circuit. The output signal (voltage) is the inverse of the input signal:

• When the input is high (+Vs) the output is low (0V).
• When the input is low (0V) the output is high (+Vs).

Any general purpose low power NPN transistor can be used. For general use R_B = 10k and R_C = 1k, then the inverter output can be connected to a device with an input impedance (resistance) of at least 10k such as a logic IC or a 555 timer (trigger and reset inputs).

If you are connecting the inverter to a CMOS logic IC input (very high impedance) you can increase R_B to 100k and R_C to 10k, this will reduce the current used by the inverter.

 

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Printed Circuit Boards (PCBs)

Bittele Electronics provides high quality mixed technology PCB assembly services. Our circuit assembly capability includes Surface-Mount parts (SMD), Through-Hole parts (THD), or any mix of them. We also offer Prototype printed circuit boardservices, for rigid or flexible, RoHS compliant, High Tg boards.

Toronto-based contract electronics manufacturer Asian Circuits Inc. has expertise in providing affordable one-stopPCB manufacturing and assembly services for both Thru-Hole and Surface Mount Technology (SMT).

Printed circuit boards have copper tracks connecting the holes where the components are placed. They are designed specially for each circuit and make construction very easy.

Designing, Creating and Soldering your own PCBs

The website build-electronic-circuits.com provides clear instructions on designing, creating and soldering your own PCBs.

Preparing a PCB ready for Soldering

1. Clean off the protective coating from the PCB using a PCB rubber or steel wool so that all the copper tracks are bright and shiny. The PCB rubber has grit in it to make it very abrasive.
   In fact the coating can be left on and it should melt away around the joints as you solder but you may get better results by removing the coating.
2. Drill the holes with a 1mm diameter bit. This is easiest with a proper electric PCB drill in a stand, but a hand-held miniature electric drill can be used if you take care to avoid twisting and snapping the small drill bit. Wear safety spectacles.
   A hand-drill is not suitable for such small bits unless you are very skilled.
3. A few may holes may need to be larger, for example preset resistors usually need a 1.5mm diameter hole. It is simplest to re-drill these special holes afterwards.
4. Check carefully to make sure you find all the holes.
   Even with experience it is easy to miss one or two!

WARNING! The small drill bits are fragile. Drill gently but firmly. If you are using a hand-held drill you must take great care to avoid twisting the drill sideways because this will snap the drill bit.

 

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Oscilloscopes (CROs)

An oscilloscope is a test instrument which allows you to look at the 'shape' of electrical signals by displaying a graph of voltage against time on its screen. It is like a voltmeter with the valuable extra function of showing how the voltage varies with time. A graticule with a 1cm grid enables you to take measurements of voltage and time from the screen.

The graph, usually called the trace, is drawn by a beam of electrons striking the phosphor coating of the screen making it emit light, usually green or blue. This is similar to the way a television picture is produced.

Oscilloscopes contain a vacuum tube with a cathode(negative electrode) at one end to emit electrons and ananode (positive electrode) to accelerate them so they move rapidly down the tube to the screen. This arrangement is called an electron gun. The tube also contains electrodes to deflect the electron beam up/down and left/right.

The electrons are called cathode rays because they are emitted by the cathode and this gives the oscilloscope its full name of cathode ray oscilloscope or CRO.

A dual trace oscilloscope can display two traces on the screen, allowing you to easily compare the input and output of an amplifier for example. It is well worth paying the modest extra cost to have this facility.

Precautions

• An oscilloscope should be handled gently to protect its fragile (and expensive) vacuum tube.
• Oscilloscopes use high voltages to create the electron beam and these remain for some time after switching off - for your own safety do not attempt to examine the inside of an oscilloscope!

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Setting up an oscilloscope

Oscilloscopes are complex instruments with many controls and they require some care to set up and use successfully. It is quite easy to 'lose' the trace off the screen if controls are set wrongly!

There is some variation in the arrangement and labelling of the many controls so the following instuctions may need to be adapted for your instrument.

This is what you should see
after setting up, when there
is no input signal connected

1. Switch on the oscilloscope to warm up (it takes a minute or two).
2. Do not connect the input lead at this stage.
3. Set the AC/GND/DC switch (by the Y INPUT) to DC.
4. Set the SWP/X-Y switch to SWP (sweep).
5. Set Trigger Level to AUTO.
6. Set Trigger Source to INT (internal, the y input).
7. Set the Y AMPLIFIER to 5V/cm (a moderate value).
8. Set the TIMEBASE to 10ms/cm (a moderate speed).
9. Turn the timebase VARIABLE control to 1 or CAL.
10. Adjust Y SHIFT (up/down) and X SHIFT (left/right) to give a trace across the middle of the screen, like the picture.
11. Adjust INTENSITY (brightness) and FOCUS to give a bright, sharp trace.
12. The oscilloscope is now ready to use!
    Connecting the input lead is described in the next section.

Further information on the controls: Timebase | Y amplifier | AC/GND/DC switch

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Connecting an oscilloscope

Construction of a co-axial lead

Oscilloscope lead and probes kit
Photograph © Rapid Electronics

The Y INPUT lead to an oscilloscope should be a co-axial lead and the diagram shows its construction. The central wire carries the signal and the screen is connected to earth (0V) to shield the signal from electrical interference (usually called noise).

Most oscilloscopes have a BNC socket for the y input and the lead is connected with a push and twist action, to disconnect you need to twist and pull. Oscilloscopes used in schools may have red and black 4mm sockets so that ordinary, unscreened, 4mm plug leads can be used if necessary.

Professionals use a specially designed lead and probes kit for best results with high frequency signals and when testing high resistance circuits, but this is not essential for simpler work at audio frequencies (up to 20kHz).

An oscilloscope is connected like a voltmeter but you must be aware that the screen (black) connection of the input lead is connected to mains earth at the oscilloscope! This means it must be connected to earth or 0V on the circuit being tested.

The trace of an AC signal
with the oscilloscope
controls correctly set

Obtaining a clear and stable trace

Once you have connected the oscilloscope to the circuit you wish to test you will need to adjust the controls to obtain a clear and stable trace on the screen:

• The Y AMPLIFIER (VOLTS/CM) control determines the height of the trace. Choose a setting so the trace occupies at least half the screen height, but does not disappear off the screen.
• The TIMEBASE (TIME/CM) control determines the rate at which the dot sweeps across the screen. Choose a setting so the trace shows at least one cycle of the signal across the screen.
  Note that a steady DC input signal gives a horizontal line trace for which the timebase setting is not critical.
• The TRIGGER control is usually best left set to AUTO.

If you are using an oscilloscope for the first time it is best to start with an easy signal such as the output from an AC power pack set to about 4V.

 

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Voltage Dividers

A voltage divider consists of two resistances R1 and R2 connected in series across a supply voltage Vs. The supply voltage is divided up between the two resistances to give an output voltage Vo which is the voltage across R2. This depends on the size of R2 relative to R1:

• If R2 is much smaller than R1, Vo is small (low, almost 0V)
  (because most of the voltage is across R1)
• If R2 is about the same as R1, Vo is about half Vs
  (because the voltage is shared about equally between R1 and R2)
• If R2 is much larger than R1, Vo is large (high, almost Vs)
  (because most of the voltage is across R2)

If you need a precise value for the output voltage Vo you can use Ohm's law and a little algebra to work out the formula for Vo shown on the right. The formula and the approximate rules given above assume that negligible current flows from the output. This is true if Vo is connected to a device with a high resistance such as voltmeter or an IC input. For further information please see the page on impedance. If the output is connected to a transistor Vo cannot become much greater than 0.7V because the transistor's base-emitter junction behaves like a diode.

Voltage dividers are also called potential dividers, a name which comes from potential difference (the proper name for voltage).

One of the main uses of voltage dividers is to connect input transducers into circuits...

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Using an input transducer (sensor) in a voltage divider

Most input transducers (sensors) vary their resistance and usually a voltage divider is used to convert this to a varyingvoltage which is more useful. The voltage signal can be fed to other parts of the circuit, such as the input to an IC or a transistor switch.

The sensor is one of the resistances in the voltage divider. It can be at the top (R1) or at the bottom (R2), the choice is determined by when you want a large value for the output voltage Vo:

• Put the sensor at the top (R1) if you want a large Vowhen the sensor has a small resistance.
• Put the sensor at the bottom (R2) if you want a large Vo when the sensor has a large resistance.

Then you need to choose a value for the resistor...

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Choosing a resistor value

OR

The value of the resistor R will determine the range of the output voltage Vo. For best results you need a large 'swing' (range) for Vo and this is achieved if the resistor is much larger than the sensor's minimum resistance Rmin, but much smaller than the sensor's maximum resistance Rmax.

You can use a multimeter to help you find the minimum and maximum values of the sensor's resistance (Rmin and Rmax). There is no need to be precise, approximate values will do.

Then choose resistor value:  R = square root of (Rmin × Rmax)
Choose a standard value which is close to this calculated value.

For example:
An LDR: Rmin = 100, Rmax = 1M, so R = square root of (100 × 1M) = 10k.

swapping over the resistor and sensor

The resistor and sensor can be swapped over to invert the action of the voltage divider. For example an LDR has a high resistance when dark and a low resistance when brightly lit, so:

• If the LDR is at the top (near +Vs),
  Vo will be low in the dark and high in bright light.
• If the LDR is at the bottom (near 0V),
  Vo will be high in the dark and low in bright light.

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Using a variable resistor

The sensor and variable
resistor can be swapped
over if necessary

A variable resistor may be used in place of the fixed resistor R. It will enable you to adjust the output voltage Vo for a given resistance of the sensor. For example you can use a variable resistor to set the exact brightness level which makes an IC change state.

The variable resistor value should be larger than the fixed resistor value. For finer control you can use a fixed resistor in series with the variable resistor. For example if a 10k fixed resistor is suitable you could replace it with a fixed 4.7k resistor in series with a 10k variable resistor, allowing you to adjust the resistance from 4.7k to 14.7k.

If you are planning to use a variable resistor connected between the +Vs supply and the base of a transistor you must include a resistor in series with the variable resistor. This is to prevent excessive base current destroying the transistor when the variable resistor is reduced to zero. For further information please see the page on Transistor Circuits.

 

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Voltage and Current

Voltage attempts to make a current flow, and current will flow if the circuit is complete. Voltage is sometimes described as the 'push' or 'force' of the electricity, it isn't really a force but this may help you to imagine what is happening. It is possible to have voltage without current, but current cannot flow without voltage.

Voltage and Current
The switch is closed making a complete circuit so current can flow.
Voltage but No Current
The switch is open so the circuit is broken and current cannot flow.
No Voltage and No Current
Without the cell there is no source of voltage so current cannot flow.

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Voltage, V

Connecting a voltmeter in parallel

• Voltage is a measure of the energy carried by the charge.
  Strictly: voltage is the "energy per unit charge".
• The proper name for voltage is potential difference or p.d. for short, but this term is rarely used in electronics.
• Voltage is supplied by the battery (or power supply).
• Voltage is used up in components, but not in wires.
• We say voltage across a component.
• Voltage is measured in volts, V.
• Voltage is measured with a voltmeter, connected in parallel.
• The symbol V is used for voltage in equations.

Voltage at a point and 0V (zero volts)

Voltage is a difference between two points, but in electronics we often refer to voltage at a point meaning the voltage difference between that point and a reference point of 0V (zero volts).

Zero volts could be any point in the circuit, but to be consistent it is normally the negative terminal of the battery or power supply. You will often see circuit diagrams labelled with 0V as a reminder.

You may find it helpful to think of voltage like height in geography. The reference point of zero height is the mean (average) sea level and all heights are measured from that point. The zero volts in an electronic circuit is like the mean sea level in geography.

Zero volts for circuits with a dual supply

Some circuits require a dual supply with three supply connections as shown in the diagram. For these circuits the zero volts reference point is the middle terminal between the two parts of the supply.

On complex circuit diagrams using a dual supply the earth symbol is often used to indicate a connection to 0V, this helps to reduce the number of wires drawn on the diagram.

The diagram shows a ±9V dual supply, the positive terminal is +9V, the negative terminal is -9V and the middle terminal is 0V.

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Connecting an ammeter in series

Current, I

• Current is the rate of flow of charge.
• Current is not used up, what flows into a component must flow out.
• We say current through a component.
• Current is measured in amps (amperes), A.
• Current is measured with an ammeter, connected in series.
  To connect in series you must break the circuit and put the ammeter acoss the gap, as shown in the diagram.
• The symbol I is used for current in equations.
  Why is the letter I used for current? ... please see FAQ.

1A (1 amp) is quite a large current for electronics, so mA (milliamps) are often used. m (milli) means "thousandth":

1mA = 0.001A, or 1000mA = 1A

The need to break the circuit to connect in series means that ammeters are difficult to use on soldered circuits. Most testing in electronics is done with voltmeters which can be easily connected without disturbing circuits.

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Voltage and Current for components in Series

Voltages add up for components connected in series.
Currents are the same through all components connected in series.

In this circuit the 4V across the resistor and the 2V across the LED add up to the battery voltage: 2V + 4V = 6V.

The current through all parts (battery, resistor and LED) is 20mA.

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Voltage and Current for components in Parallel

Voltages are the same across all components connected in parallel.
Currents add up for components connected in parallel.

In this circuit the battery, resistor and lamp all have 6V across them.

The 30mA current through the resistor and the 60mA current through the lamp add up to the 90mA current through the battery.

 

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