What is chopper

First of all, we should check what chopper exactly means and after that where it mostly used.

 What is a chopper?

As we know that a chopper is one type of electronic circuit used to refer numerous types of electronic switching devices and used in power control and signals applications. 

 A chopper is a static device and it converts fixed dc input voltage to a voltage to a variable dc output voltage directly.

A chopper is basically a DC to DC converter whose main function is to create an adjustable DC voltage from a fixed DC voltage source through the use of semiconductors.


A chopper is more efficient as they involved in only one stage conversion. The future electric automobiles are likely to use the chopper for their speed control and also braking.


A chopper is considered as a DC equivalent of an AC transformer since it behaves in an identical manner.


The chopper used in trolley cars, marine hoists, forklift trucks, and also a mine hauler. The chopper is the dc equivalent to an ac transformer having continuously variable to a turn ratio. Like a transformer, a chopper can be used to step up or step down with the fixed DC input voltage.

 In power electronic system the conversion from fixed dc voltage to an adjustable dc output voltage, through the use of semiconductor devices, can be carried out by the two types of dc to dc converters like ac link chopper and also a dc chopper. 


Chopper circuits are very widely used in power electronics as also numerous electronics circuits as given below. 

  • SMPS terms
  • DC DC converters
  • Amplifiers
  • Filters
  • DC motor speed control
  • VFD drives motors
Applications of chopper : 
  • Switched mode power supply 
  • DC to DC converter 
  • Class D electronic amplifier 
  • Switched capacitor filter 
  • Variable frequency drive
  • DC voltage boosting 
  • Battery operated electric cars
  • Battery chargers 
  • Railway traction 

FIR filter block diagram

In the digital signal processing system, the use of  FIR short form is one type of filter whose impulse response is of finite duration, the reason of it settles zero in finite time. This is a contrast to IIR filter design, which has internal feedback and may continue to respond indefinitely. 

A discrete time FIR filter of N number of order and the top part is an N stage delay line with total N+1 taps to shown in the figure. Each of unit delay is a Z-1 type of operator in the Z transform notation. 

The output y of a linear time-invariant system is determined by conveying its input signal x with its impulse response b. 


For a discrete-time FIR filter, the output is depend on a weighted sum of the current and finite number of previous values of the input signal.

The operation is described by the following equation, which defines the output sequence of y[n] in terms of its input sequence of x [n] given below.

Y[n] = b0 x[n] + b1 x[n-1]  + b2 x[n-2] …………bn x[n-N]
           N
Y[n] =  ∑ bi x[n-i]
          I=0

Where, 

x[n] = input signal
y[n] = output signal

DC chopper

A chopper is a static device that converts fixed dc input voltage to a variable dc output voltage directly.

 A chopper may be thought of as dc equivalent of an ac transformer so that they behave in an identical manner. As chopper involve that one stage conversion, these are more efficient for the circuit.

Chopper is now being all over for rapid transits systems. Chopper systems offer smooth control,  fast response, high efficiency, and regeneration.

The power semiconductor devices used for a chopper circuit can be force commutative thyristor, power BJT, IGBT, power MOSFET. 

As stated above, a chopper is dc equivalent to an ac transformer having continuously variable turn ratio. 

 A  transformer, a chopper can be used to step up or step down for the fixed dc input voltage. As a step-down dc chopper is more common, the term dc chopper or chopper would mean a step-down dc chopper.

Chopper application

A  terms chopper is considered as DC equivalent of an AC transformer since it behaves in an identical manner. It can be used many more electrical device like the electric car, mine hauler, Forklift trucks etc. Here this articles gives information about chopper application to know more details about it.
  • Chopper is used for DC motor control
  • Solar and wind energy conversion
  • It has more efficient as they involve in one or more stage conversion
  • Dynamic  break
  • Forklift trucks, mine hauler, trolley cars
  • HVDT
  • It also used in the electric car
  • Speed control and braking
  • Airplane and spaceships, where onboard regulated DC power supplies are required
  • Chopper supply circuit are used as power supplies in computers, commercial electronics, electronics instruments
  • DC voltage boosting
  • Battery chargers
  • Onboard regulated the dc power supply

Type E chopper

As we that a chopper is one type of electronic circuit used to refer numerous types of electronic switching devices and used in power control and signals applications. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc. Now let us check it out the information about type E chopper to know more details about the chopper.

 The power diagram for a four-quadrant chopper is shown in the figure. 
  • It consists of four semiconductor switches CH1 to CH4 and also four diode D1 to D4 in anti-parallel.
  • The numbering of chopper CH1,...CH4  corresponds to their respective quadrant operation.
  • For example for first quadrant operation, only chopper CH1 is operated for second quadrant operation, only CH2 is operated and so on. 
  • Working of this chopper in the four quadrants is explained as under four quadrants is given below.
First quadrant :
  • For 1st quadrant operation of the figure shown chopper CH4 is kept ON, CH3 is kept off and chopper CH1 is operated.
  • With chopper CH1, CH4 on load voltage V0 = Vs and load current I0 begins to flow. 
  • Here both voltage, as well as current V0 and I0, are positive giving first quadrant operation.
  • When CH1 is turn off positive current freewheels through chopper CH4, D2.
  • In this manner, both voltage and current V0, I0 can be controlled in the first quadrant.
Second quadrant :
  • Here CH2 is operated and CH1, CH3, and CH4 kept off.
  • With CH2 on, reverse current flows through L, CH2, D4, and E inductance L stores energy during the time CH2 is on.
  • When CH2 is turn off current is fed back to the source through diodes D1, D4. 
  • Note that here the voltage (E+L di/dt) is more than the source voltage of Vs.
  • As load voltage V0 is positive and I0 is negative, it is the second quadrant operation of the chopper, Also power is fed back from load to source.
  • So this quadrant, configuration operates as a step-up type of chopper.
Third quadrant :
  • For third quadrant operation, chopper CH1 is kept off, chopper CH2 is kept on and CH3  is operated.
  • Polarity of load emf E must be reversed for this quadrant working.
  • When chopper CH3 is on, the load gets connected to source Vs so that both V0, I0 are negative leading to third quadrant operation.
  • When chopper CH3 is turn off, negative current freewheels through CH2, CH4. 
  • In this manner V0 and I0 can be controlled in the third quadrant.
  • Here chopper operates as a step-down, the chopper operates as a step down a chopper.
Fourth quadrant :
  • And last here chopper CH4 is operated and also some other devices are kept off. Load emf E has its polarity and its as shown in figure for its operation in the fourth quadrant.
  • With chopper CH4 on, positive current flows through chopper CH4, D2, L and E, inductance L stores energy during the time CH4 is on.
  • When chopper CH4 is turn off current is fed back to the source through D2 and D3. 
  • Here load voltages negative while load current is positive, leading to the chopper operation in the fourth quadrant. 
  • Also, the power is fed back from the load to the source side. 
  • Here  chopper operates as a step up chopper.

Type C chopper

As we know that a chopper is a static device that converts fixed dc input voltage to a variable dc output voltage directly. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc.

This type of chopper is also called as two quadrants called type A chopper. This type of chopper is obtained by connecting type A and type B choppers in parallel as shown in the figure given below.
  • The output voltage V0 is always positive because of the presence of a freewheeling diode called FD across the load. 
  • When chopper CH2  is on, or freewheeling diode conducts, output voltage V0 = 0 and in case chopper CH1 is on or diode D2 conduct, the output voltage is equal to the voltage V0 =  Vs
  • The load current called I0 can, however, reverse its direction. 
  • Current flows in the arrow direction marked in the figure.
  • The load current is positive when CH1 is on or FD operate together as type A chopper in the first quadrant. 
  • Likewise, CH2 and D2 operate together as type B chopper in the second quadrant.
  • Average load voltage is always positive but the average load current may be positive or negative as explained above.
  • Therefore, power flow may be from the source to load or from load to source.
  • So in Chopper CH1 and chopper CH2 should not be on simultaneously as this would lead to a direct short circuit on the supply lines.
  • This type of chopper configuration is used for motoring and regenerative braking of dc motors
  • This type of operating region of this type of chopper is shown in figure second by the hatched area in the first and second quadrants.   

Type B chopper

As we know that a what chopper can operate in any of the four quadrants by an appropriate arrangement of semiconductor devices. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc.

 Power circuit for this type of chopper is shown in the figure. Note that load must contain a DC source of E, like a battery in this chopper circuit.
  • When the chopper is in V0 = 0 but load voltage E drives current through L and chopper 2. Inductance L store energy during Ton of a chopper. 
  • When chopper is off mean  V0 = ( E + L di/dt ) exceeds source voltage Vs.
  • As result diode D2 is forward biased and also begins conditions, thus allowing power to flow to the source.
  • The chopper may be ON or OFF, current I0 flows out of the load, current I0 is therefore treated as negative (-ve side). 
  • Since voltage V0 always positive and current I0 is negative, power flow is always from load to source. 
  • As load voltage V0 = (E+L di/dt) is more than a source voltage of  Vs.
  • Type B chopper is also called a step-up chopper.

  • Both type A and type B chopper configuration have a common negative terminal between their input as well as output circuits.

Type A chopper

We all know that a chopper definition can operate in any of the four quadrants by an appropriate arrangement of semiconductor devices. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc.

It is observed that the chopper circuit of the figure also types A chopper. 
  • When the chopper is on V0 = Vs and current i0 flows from in the arrow direction shown. 
  • When the chopper is in off  V0=0 and i0 in the load continues flowing in the same direction through freewheeling diode FD, shown in the figure. 
  • It is thus seen that the average values of both load voltage and current  V0 and I0 are always positive.
  • And this shown by the second figure by the hatched area in the first quadrant of  V0 - I0 plane in the figure.
  • The power flow in type A chopper is always from the source side to load side. This chopper is also known as the step-down chopper as average output voltage V0 is always less than the input dc voltage Vs.

Half adder and full adder difference

we all know that a half adder is a one types of combinational logic circuit with two input and also have two output wheres the full adder is add three one-bit binary numbers, two is operands and a carry bit but in output is to be two numbers, sum and carry bit, this is the main difference between them. This article gives information about the difference between the half adder and full adder to know more details about it.

Definition :
  • Half adder: Half adder is a combinational logic circuit which adds two 1 bit digits
  • Full adder: Full adder is a combinational circuit which adds three 1 bit digits
Hardware :
  • Half adder: It consists of one EX-OR gate and one AND gate 
  • Full adder: It consists two EX-OR, two AND gate, and one OR gate
Carry addition :
  • Half adder: Carry generated from a previous addition is not added in the next step
  • Full adder: Carry generated from a previous addition in the next step
Application : 
  • Half adder: Calculator, computers, digital measuring devices etc
  • Full adder: Multiple bit addition, digital processor

Half adder block diagram

Half adder is a one types of combinational logic circuit with two input and  also have two output. It is basic building block for addition of two single bit  numbers.  This circuit has two outputs called as sum and carry.   

The half adder circuit designed to add two single bit binary numbers A and B. Hence the truth table of a half adder is shown in fig. 
       -          -
S = AB + AB

 Using Karnaugh maps :

 

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Advantages and disadvantages of FIR and IIR filters

FIR stands for finite impulse response. Most of the FIR full form filter is that linear phase filter When the linear phase filter is desired an FIR filter is usually used. Here this article gives information about the advantages and disadvantages of FIR as well as IIR filters to know more details about it. 

Advantages of  FIR filters :
  • FIR filter is always stable
  • It is simple
  • Design complexity generally linear
  • FIR filter are having linear phase response
  • It is easy to optimize
  • Non causal
  • Transient have a finite duration
  • Quantization noise is not much as a problem
  • Round of noise error is minimum
  • Both filtering recursive, as well as nonrecursive filter, can be also designed using FIR designing techniques
  • For designing of a filter having an arbitrary magnitude response; FIR filter designing techniques can be easily applied
  • Good performance
  • Robust
  • The necessity of computational techniques for filter implementation
  • A requirement of large storage
  • Incapability of linear phase response
Disadvantages of FIR filters :
  • Large storage requirements
  • Can not simulate prototype analog filter
  • For the implementation of FIR filter complex computational techniques are required to implement
  • It is hard to implementation than IIR
  • Expensive due to a large order
  • Require more memory
  • Time-consuming process
IIR stands for infinite impulse response. IIR Filter has a lower filter order then a corresponding FIR filter. Here this article also gives information about the advantages and disadvantages of  IIR filters to know more details about it.

Advantages of IIR filters :
  • It has a stable design
  • An IIR filter has a lesser number of side lobes in the stop band then FIR filter with the same number of parameters
  • Implementation of an IIR filter involves fewer parameters 
  • Less memory requirement
  • Lower computational complexity
  • Analog frequency and digital frequency are linearly related
Disadvantages of IIR filters :
  • This filter is useful only when the analog filter is bandlimited
  • They are harder to implement using fixed-point arithmetic, such as noise generated by calculations and also a limit cycles
  • They are more susceptible to the problem of line finite length arithmetic
  • They don't offer the computational advantages of FIR filter for the multi-rate application system
Explore more information:

IIR filter example

IIR filter short form is for infinite impulse response. In IIR filter design that are following criteria should be satisfied by designing the digital filter in the analog domain and transforming into a digital domain.

 The transfer function of analog filter is :

H(s) = 3 / (s+2) (s+3) with Ts = 0.1 sec

Design the digital IIR filter using BLT.

Answer :

H(s) = 3 / (s+2) (s+3)........................(1)

In BLT H(Z) is obtained by putting :

s = 2/Ts [ Z-1/Z+1] here Ts = 0.1 sec

s = 2/0.1 [ Z-1/Z+1]  

s = 20 [ Z-1/Z+1]  

Putting this value in equation (1) we get,

H(Z) = 3 / [ 20*(Z-1/Z+1)+2] [  20*(Z-1/Z+1)+3]

H(Z) = 3 / [(20Z-20/Z+1) + 2] [ (20Z-20/Z+1 ) + 3 ]

H(Z) = 3 (Z+1) (Z+1) / (20Z-20+2Z+2) (20Z-20+3Z+3) 

H(Z) = 3 (Z+1)2 /  506Z2-374Z-414Z+306
-
H(Z) = 3  (Z2+ 2Z +1 )/  506Z2-788Z+306

H(Z) =  (Z2+ 2Z +1 )/  168.67Z2-262.67Z+102

This function required a function for digital IIR filter 

Z transform inverse

If we want to analyze a system, which is already represented in the frequency domain, a discrete time signal then we go for inverse Z transformation.

Mathematically it can be represented as : 
x(n) = z-1 X(Z)
x(n) = Z-1 X(Z)

Here x(n) is the signal in time domain and X(Z) is the signal in the frequency domain to be represented.

And here also define if we want to represent the above equation in integral format then we can write it as

x(n) = (1/2∏j) ∫ X(z) Z-1 dz

Here the integral is over close path C. This is within the region of conversions (ROC) of the x(z) and it does contain the origin. Now here this article also gives the information about how to find inverse Z transform.

Method to find Inverse Z - transform :

We follow the following four-way to determine the inverse Z transformation system.

Inverse Z transform using long division method

While carrying out the long division method, it always converts the given expression in the simplest form. That means as far as possible, it should be in form of Z divided by some polynomial. |Z| > 1 it is causal sequence. For the causal sequence the denominator polynomial should have maximum power of Z transform on its left. Thus the given expression is in the total proper form.

Find inverse Z transform of  X(z) is = Z/Z-1   |Z|>1 



X(Z) = 1 + Z-1 +  Z-2  +  Z-3+..........

             ∞
X(Z) = ∑ x(n) Z-n
          n=0 

X(Z) is = x(0) + x(1) Z-1 + x(2) Z-2  + x(3) Z-3


X(n) =  {x(0) ,  x(1), x(2), x(3) }

x(n) = { 1, 1, 1, 1 }

x(n) = u(n)


Z-1{Z-1/Z-1} = u(n)

This is a standard Z transform pair.

Z transform partial fraction expansion

Partial fraction expansion method is possible only when Z transform definition which is rational in nature, That means they are expressed of two polynomials.

X(Z) = N(Z) / D(Z)
= b0 +  b1  Z-1  + b2  Z-2   + …….+ bM Z-M  /  a0 +  a1  Z-1  + a2  Z-2   + …….+ aN Z-N

  b0 ,  b1  , b2   , bM =  Coefficients of numerator 

 a0 , a1  ,  a2  ..... aN  =  Coefficients of Denominator

 M = Degree of numerator 

N =  Degree of denominator
N(Z) = Numerator  polynomial
D(Z) = Denominator polynomial

Step to follow the partial fraction expansion method :


Step 1: Check whether the given function is the proper form or not. The function is said to be in proper form when the following conditions are satisfied. 

  • The coefficient a0 in the above equation should be equal to 1. If  a0  not equal to 1 then the polynomial is adjusted accordingly.
  • In equation a0  not equal to 1 and the degree of numerator should be less than the degree of the denominator(M<N). If this condition is satisfied then the long division is carried out to make M<N.
Step 2: Multiply the numerator and denominator by ZN. That means to convert the function in term of the positive power of Z.
Step 3 :  Obtain  the equation X(Z) / Z

Step 4: Factorize the denominator and obtain the roots. Then the denominator will be in the form 

(Z - P1 ) (Z - P2 ) (Z - P3 )............(Z -PN )

Here P1  P2  P3  ........PN is called as poles.

Step 5 :  Write down the equation in partial expansion form as follows :
X(Z) / Z =  A1 /  Z - P1  + A2 / Z - P2  + .............+   AN / Z - PN
A1, A2,  A3 .....AN  are coefficient. the coefficient AK is  calculated as 
 AK =  (Z - PK ). X(Z) / Z  | where Z=PK

Step 6 : By calculating  transfer  of a1, a2,  a3 .....an   z to R.H.S of equation. Now we standard from pair to obtain inverse Z transform

x(n) = IZT { Z /  Z - PK  } = (PK)n u(n) if ROC : |Z| > | PK |
that means causal sequence 

AND 
x(n) = IZT { Z /  Z - PK  } = - (PK)n u(-n-1) if ROC : |Z| < | PK |
that means anticausal sequence 

 Now let us check it out the example of partial fraction method to learn more details about this article.
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