Thyristor

THYRISTOR A thyristor, commonly known as SCR (Silicon Controlled Rectifier) is basically a four – layer pnpn device that has three electrodes ( a cathode, an anode and a control electrode called the gate).

Current – voltage characteristics for an SCR are shown below:

When an SCR is reverse – biased (anode negative with respect to the cathode), the centre junction is reverse – biased too and only a very low reverse current flows through the device. If the voltage exceeds the reverse breakdown voltage, the reverse current increases rapidly. During forward – bias operation (UAC is positive) the pnpn structure of the SCR is bistable (OFF state – high impedance, ON state – low impedance. In the forward – blocking state (OFF) a small forward current, called the leakage current, flows through the device. The magnitude of this current is approximately the same as that of the reverse – blocking current. At the forward breakover voltage the current increases rapidly and the SCR switches to the ON state, with a very low (about 1V) forward ON – state voltage drop. In the ON state the forward current is limited primarily by the load impedance. The SCR will remain in this state until the current and then reverts back to the OFF state. The breakover voltage can be varied by injection of a signal to the gate. As the gate current is increased, the value of breakover voltage becomes less until the device goes into the ON state. This enables an SCR to control a high power load with a very low – power signal.

Apart from the gate control, an SCR can also be triggered (turned ob.): - by light incident onto the gate – cathode junction (phototyristor) - when the anode – cathode voltage increases very rapidly - when the temperature significantly increases. The operation of the SCR can easily be explained using its equivalent two – transistor circuit.

When a current is applied to the gate, T2 turns on and its collector drives the base of T1. T1 turns on and its collector drives the base of T2.

The gate current is only required to trigger the device and can later cease to zero, because upon triggering both transistors drive each other. In order to turn off an SCR, the anode current must decrease below the holding current. In DC circuits some additional components have to be used to ensure this. In AC circuits an SCR turns off when the supply voltage (anode voltage) crosses zero towards negative values. Some applications of thyristors Thyristors are mainly used in power electronics. Power electronics deals with the application of electronics devices and associated components to the conversion, control and conditioning of electric power. The primary characteristics of electric power which are subject to control include its basic form (AC or DC), its effective (RMS) voltage or current, frequency and power factor. The control of electric power is frequently desired as a means for achieving control or regulation of the speed of a motor, the temperature of an oven, the rate of an electrochemical process, the intensity of lighting etc. One of the simplest applications is a controlled rectifier, which can be obtained any rectifier circuit by replacing the diodes with SCRs. The figure below shows a full – wave controlled rectifier and the waveforms that illustrate its operation.

The average output voltage of this circuit is: U LAV =

Π U 1 U m sin ω td ω t = m (1 + cos α ) ∫ Πα Π

By varying the firing angle for both SCRs the average rectified voltage can be changed from 2Um/Π (uncontrolled rectifier) down to zero.

Note that the output waveform includes harmonics that may deteriorate the performance of various electronic devices. Many loads such as heaters, lamps etc. Do not require rectified supply voltage. In such cases power can be directly controlled in AC circuits by use two SCRs connected in anti – parallel, as shown below.

Inverters are used to convert DC into AC. This is accomplished through alternating application of the source to the load, achieved through proper use of controllable switches. Two simple structures of inverters are shown in the following figures.

push – pull inventer

bridge inventer

In the push – pull inverter the DC supply source is periodically connected to each half of the primary, producing a rectangular waveform across the load. In the bridge inverter, which requires no power transformer, the SCRs are turned on in pairs, T1T4 and T2T3. The capacitor is necessary to ensure the proper operation of the circuit, i.e. to guarantee the commutation of SCRs. With T1 and T4 in the ON state the capacitor is charged with the polarity shown in the figure. When T2 and T3 are turned on, the voltage across the capacitor reverse biases both T1 and T4. To produce a sinusoidal waveform of the output voltage, more sophisticated techniques are used. Inverters are used, in particular, for control of electric motors, in uninterruptible power supplies (UPS) and in many other applications. FEEDBACK Feedback is a commonly used method of modifying the parameters of electronic circuits. The circuit shown in the figure illustrates a generalised view of feedback, with an amplifier with gain k, and a feedback circuit which returns a fraction β of output to the input.

The returned signal Sf is summed with the input signal Sin to produce the input to the amplifier Si. The input Si is often referred to as the error signal.

The signal at any node of the circuit can be either voltage or current. Some basic definitions which apply are:

k

f

S out S in

=

β =

S

f

S out

k =

is the open – loop gain, that is without feedback

S out Si

is the feedback factor, that is a fraction of the returned signal

is the closed – loop gain, that is with feedback applied

For the general circuit the following relationships are valid: Si =Sin +Sf Sout =kSi Sf = βSout

Substituting gives:

S out = k (S in + β S out

)

The overall gain (closed – loop gain) is defined as: k

f

=

S out k = 1 − kβ S in

or

k

f

=

k 1+T

Where kβ is the loop gain, - kβ is often referred to as the loop transmission T, and 1- kβ is known as the return difference (desensitivity). Provided that 1- kβ>1 (kβ<0, either k or β negative) then kf < k and the feedback is said to be negative. If 1- kβ<1 then kf > k and the feedback is said to be positive. The return difference 1- kβ can approach zero, and the closed – loop gain towards infinity. Under these circumstances the circuit becomes unstable and oscillates. Negative feedback offers a number of advantages and some of the more important are:

-

improved gain stability reduced noise and distortion improved frequency response modified input and output impedance levels

These advantages are obtained at the expense of a reduction in the overall gain. However, amplifiers are often designed to have a gain which is considerably higher than is required, and negative feedback is used to reduce the gain to the required level with a subsequent improvement in the overall performance of the circuit. Positive feedback, on the contrary, has some disadvantages and is rarely used in electronic circuits, mainly in oscillators. Note that, in general, the phase relationship between the input and output of both the amplifier and the feedback network varies with frequency. This means that it is possible for the feedback to change from being negative to positive and the amplifier may oscillate. To prevent this happening, special frequency compensation method must often be applied, especially in wide – band amplifier circuits. Types of feedback Since both the output and the input can be characterised by either voltage or current, then four possible types of feedback may be sampled and either a voltage or current may be returned to the input. The four feedback configurations are shown below.

Notice different dimensions of the transfer parameter for the amplifier and the feedback network in each case. In particular:

k=

u out = ku ui

is the voltage gain

k=

u out = Rm ii

is the transresistance

k=

iout = Gm ui

is the transconductance

k=

iout = ki ii

is the current gain

Effects of negative feedback Gain stability Let us start with an example, assuming that the open – loop voltage gain and the feedback are: β = 0.1

K=-10000 kf =

Then

k − 10000 = = − 9 .990 ≈ 1 1 − k β 1 − ( − 10000 ) ⋅ 0 .1

Now let us assume that the open – loop voltage gain increases by 100% (e.g. due to the manufacturing spread). − 20000

= − 9 . 995 ≈ − 10 The k f = 1 − ( − 20000 ) ⋅ 0 . 1 n

The increase in overall gain is

9 .995 − 9 .990 ⋅ 100 % = 0 .05 % 9 .990

Thanks to negative feedback a 100% variation bas been reduced to 0.05%. If the amplifier were designed to have a gain of 10 without negative feedback then there could be large variations of gain as a result of differences in the active components. A common design practice is to arrange the loop gain to be much greater then unity.

Then:

kf =

k k 1 ≈ =− β 1 − kβ − kβ

According to this equation the gain of complete amplifier is independent of the open – loop gain. The feedback factor β is usually determined by passive components, for example resistors, which are much more stable than active devices. Input and output resistance Both the input and the output resistance are affected by the application of negative feedback. With series feedback the voltage returned to the input opposes the input voltage and the input current is less than it would be without feedback. This situation is shown in the following figure.

The input resistance of the complete amplifier is defined as

R inf =

Rinf =

ui − u f iin

=

u in i in

u i − kβu i u i = (1 − kβ ) iin iin

where ui/iin is the input resistance of the amplifier without feedback. Rinf = Rin (1 − kβ ) > Rin

where kβ < 0

The input resistance with series feedback is increased, regardless of the output configuration (whether the feedback signal is proportional to the output voltage or he output current). For the shunt feedback: Rinf =

uin u uin uin = in = = iin ii − i f ii − kβii ii (1 − kβ )

Rinf =

Rin 1 − kβ

The input resistance with shunt feedback is reduced.

To determine the output resistance of an amplifier with feedback, we will use an equivalent circuit of a voltage (for voltage sampling) or a current (for current sampling) amplifier.

The output resistance can be determined as the ratio of the open – circuit output voltage and the short – circuit output current.

For the voltage sampling configuration we get:

Rout u

out

op

.

c

=

kS

i

=

k

(

S

in

+

S

)

f

=

k

(

S

in

=

f +

β

U

out

uout

op.c

iout

op

.

c

sh.c

Rout

f

=

u out

op .c

iout sh.c

Uout op.c = kSi = k(Sin + Sf) = k(Sin + βUout op.c)

uout

iout

Rout

op.c.

sh.c.

f

=

=

=

k Sin 1− kβ

kSi kSin = Rout Rout

Rout 1− kβ

because sf = 0 (uout = 0)

kβ < 0 for negative feedback

The output resistance for voltage sampling with output resistance with either series or shunt connection at the input is decreased. It can be shown in a similar way that the output resistance for current sampling with either series or parallel connection at the input is increased: Rout f = Rout (1-kβ)

Reduction of noise and distortion

To study the effect of negative feedback on the noise, let us consider a two – stage amplifier noise signal introduced into the signal path at different nodes.

With no feedback applied Sout =k1k2 (Sin = n1 ) + k2n2 + n3 With negative feedback network connected: S out =

k1 k 2 k2 1 ( S in + n1 ) + n2 + n3 1 − k1 k 2 β 1 − k1 k 2 β 1 − k1 k 2 β

Comparing individual terms of both expressions it may seem that there is no improvement in the signal to noise ratio. However, for given levels of noise entering the circuit and a required value of the output signal, the contribution of individual noise signal into the output signal can be significantly reduced. If, for example n3=1V (e.g. ripple of the supply voltage), Sout=10V (e.g. maximum voltage required to drive a loudspeaker), |k1|=|k2|=100 and β=0.1, then the ripple present in the output signal becomes n3=1V with the feedback loop open. 1 n 3 = 1mV 1 − k1 k 2 β

with the feedback loop closed

This reduction in noise level is achieved at a cost of signal amplification. With no feedback the input signal should be 1mV (Sout/k1k2). With negative feedback applied the amplitude of the input signal should be increased to 1V (kf=10). Notice that the most efficient reduction is achieved for noise signal introduced into the circuit near its output. Feedback cannot reduce noise which enters with the signal from the source. The same conclusions can be drawn for the effect of negative feedback on non-linear distortion. Non-linear distortion manifests as harmonics that appear in the output signal of an amplifier. These harmonics can be considered as external distributing signal n3 that add to the fundamental harmonic at the output node. Consequently: h

f

=

h 1 − kβ

where h is the harmonics distortion coefficient for the open – loop amplifier.

Notice that negative feedback cannot reduce distortion that results from the transistor operating point entering the cut – off or saturation region. In such cases the gain of the amplifier becomes very low (=o) and the condition kβ>>1 is no longer valid. Bandwidth Let us assume that the open – loop transfer function of an amplifier is described by the first – order function:

k0

k ( jω ) =

1+ j

ω ωH

Where ko is the gain for low frequencies and ωH is the upper 3dB frequency. Substituting this expression to the formula for the closed – loop gain we get: k0 k f ( jω ) =

k = 1 − kβ

1+ j 1−

ω ωH

k0 1+ j

ω ωH

k0

=

β

1+ j

ω − k0 β ωH

k0 1 − k0 β

= 1+ j

ω

ω H (1 − k 0 β )

=

kf0 1+ j

ω ω Hf

The closed – loop amplifier is also described by the first – order low – pass transfer function. Notice that:

k f 0 ⋅ ω Hf =

k0 ⋅ ω H (1 − k 0 β ) = k 0ω H 1 − k0 β

In other words the closed – loop upped 3dB frequency is inversely proportional to the closed – loop gain at low frequencies. Taking the first – order transfer function of a high – order amplifier we can prove in a similar way that the closed – loop lower 3dB frequency becomes

fL 1 − kβ In conclusion, at the expense of gain reduction by a factor of (1- kβ) negative feedback reduces the lower 3dB frequency by the same factor. These effects are illustrated graphically in the following figure. f Lf =

Miller effect and bootstrap Let us determine the impedance seen by a voltage that has an impedance connected between its input and output as shown in the figure below.

Assuming that the amplifier is ideal (Rin → ∞, Rout = 0) we get: Z in =

U1 I1

I1 =

U 1 − kU 1 Z

Z

in

=

Z 1− k

The impedance is scaled by a factor depending on he gain of the amplifier. If a capacitor is connected as Z between the input and output of an inverting amplifier (k<0), the capacitance seen by the source is: Cin = C (1-k) = C(1+|k|)

This effective increase of C in known as the Miller effect. It is often used to linearize the output waveform of ramp generators. On the other hand, it is often harmful because a large increase in the input – to – output parasitic capacitance of an amplifier considerably decrease the bandwidth. If Z = R and k approaches 1, then Zin = Rin → ∞

This effect is know as bootstrapping. This technique is often used to dynamically increase the resistance of a resistor. Another application deals with the linearization of the output waveform in ramp generators as shown below.

I=

U + E −U E = = const R R

u (t ) =

1 C

∫

Idt =

E ⋅t RC