Circuits with Feedback and Oscillators - Report Example

Circuits with Feedback and Oscillators Response to task 1Question Types of feedback Introduction The occurrence of an oscillator is such that part of the amplifier signal is send back to the input of that very amplifier (Ellinger, 2008). Because of this, the signal is amplified and resent back to the input upon which it becomes amplified once more. The process repeats itself several times ultimately leading to a loud noise from the speaker. This process of sending part of the amplifier output signal back to the input of is often referred to as feedback (Ellinger, 2008). As widely cited, as far as amplifiers are concerned, there are generally two types of feedback. These are positive or regenerative feedback and negative or degenerative feedback (Ellinger, 2008). The difference between two types of feedback entails whether the feedback signal is out of phase or in phase with an input signal. The term feedback can also refer to process through which information on future or present events tend to affect similar events in future while a feedback amplifier is that which the fraction of output energy get fed back to an input of that same circuit. As widely cited, there are two types of feedback. These are negative also referred to as inverse or degenerative feedback and the positive also referred to as direct or regenerative feedback. The different between the two types of feedback is basically on whether the feedback signal is out of phase or in phase with an input signal. Negative feedback Negative feedback refers to the feedback signal that is 180 degrees out of phase with respect to that of the input signal. Generally, negative feedback can be divided into two: voltage feedback and current feedback. As often is the case, the current feedback is applied purposely to reduce the input amplifier. However, there are cases where both feedbacks may exist in a circuit. In such a case, both current voltage would be feedback towards the input in parallel or series. This, therefore, imply that the feedback would be represented as series-voltage feedback, series-current feedback, shunt current feedback, and shunt- voltage feedback. Arguably, negative feedback makes a gain in a circuit to be stable. Mathematically, it can be shown that A1= AB + A/1. For cases where AB>> 1 the expression reduces to A1=1/B. The mathematical expression implies that such a circuit is quite independent from the internal gain. It is worth noting that the negative feedback is has a many merits. It has been cited as being the best in creating the practical circuits due to its characteristic nature of being able to set rates, gains, alongside other significant parameters. Moreover, the negative feedback can make the circuits self-correcting and stable. By and large, the fundamental principle of the negative feedback is such that the output drives in such a direction creating an equilibrium condition. For an op-amp circuit without a feedback, there is lacking a corrective mechanism. The output voltage shall become saturated with a tiniest amount of the differential voltage that is applied in the in). It has also been noted that negative feedback will make a gain in a circuit to be stable. Moreover, research has it that the negative feedback is a fundamental principle as far as the operation of an amplifier is concerned. This is based on the fact that it can be used in creating practical circuits given its characteristic of setting up rates, gains, alongside other significant parameters. Thus, an op-amp circuit without a feedback lacks a corrective mechanism and this causes the output voltage to become saturated with a tiniest amount of the differential voltage that is applied in the inputs. More significantly, it is argued that negative feedback can make the circuits self-correcting and stable given that operates on a principle that state that the output drives in such a direction creating an equilibrium condition. It is also evident from research that negative feedback helps in limiting the input signal of an amplifier, thereby, improving its fidelity. It can, as well be used for purposes of increasing the amplifier’s frequency response. This way, the amplifier’s gain does decrease whenever the frequency limit is approached. In practice, with the negative feedback in use, the feedback signal reduces while the input signal increases. This implies that at certain limits of the frequency response of an amplifier, a smaller feedback implies that the gain with feedback or the effective gain. This helps improve frequency response of an amplifier. Generally, negative feedback can be used in provide gain stability, reduce on no-linear distortion, increasing bandwidth, reducing noise, increasing the input impedance while decreasing the output impedance, and, therefore, used in most of the amplifier circuits. The positive feedback is the type of feedback in which, the current or voltage feedback is applied in order to increase the voltage input. It is commonly referred to as direct or regenerative feedback. Applying a positive feedback in a circuit, make it possible to take a portion of the output signal back to the input especially for the non-inverting signal. The lack of a positive feedback in a circuit slows down the response of the open loop detectors. This way, on the overall, the positive external feedback could be applied although somewhat different from the internal feedback which could be set in the latter purpose-designed stages. This has a far reaching influence on the zero-crossing point of detection accuracy. As widely cited, positive or Regenerative feedback is said to occur whenever the feedback signal happens to be in phase with an input signal. There are various advantages attributed to positive feedback. First, a positive feedback characteristically known for being able to cause an increase in the gain of an amplifier, contrary to the negative feed-back, which causes a reduction in the gain of the amplifier. Response to Task 1Question 2. A circuit with negative feedback. Figure 1.1: Negative feedback The circuit above show that whenever the feedback current or voltage is applied with view to have the input signal weakened (with the feedback being out of phase), it is referred to as negative feedback. In this case, the feedback network combines with a fraction of the output signal back to the input. Given that the output signal appears to be 180 degrees out of phase with the given output signal, then it leads to a negative feedback. The figure below shows a circuit employing a negative feedback. Response to Task 1 Question 3. In order to build a Wien-Bridge oscillator, there is need to put into consideration a number of factors. To start with, there is need to make sure that there is a Frequency Control although, the number of the frequency decades that is required for constructing a Wien-Bridge Oscillator varies. In most case, a minimum of three frequency decades are used. In this regard, the frequency decade must always cover at least an audible spectrum that is known to range from 20 Hz to about 20 kHz. It should also be noted that there is needed a two-gang variable capacitor alongside a two section variable resistor. These are often used for purposes of adjusting the frequency of the circuit. Moreover, for one to start the process of building a practical Wien-Bridge Oscillator, he or she requires oscillators that comprise a differential amplifier constituted by a relatively large open-loop gain. As if not enough, one needs to have an R-c network to be used in the determining of frequency, as well as a non-linear resistive network for purposes of amplitude stabilization. The Effects of applying the feedback to a single and multi-stage circuits. Feedback amplifiers are those amplifies that have a part of output energy getting fed back to an input of that same circuit. For a positive feedback to occur, the feedback signal has to be in phase with that of the input signal and the signal and this makes it an additive. However, for the feedback signal that is 180 degrees out of phase with respect to that of the input signal, it becomes a negative feedback. The negative feedback amplifiers find a lot of application. In particular, in a multi-stage circuits, applying a feedback has a significant effect. First, it reduces the extremely high gain to a somewhat lower usable amount. Second, applying the feedback causes a reduction in the distortion. Third, the feedback in a multi-stage circuit causes an increase in the response of the upper frequency. It also causes an increase in the input impedance. Last but not least, applying a feedback in a multi-stage circuit leads to a reduction in the output impedance. Response to Task 2 Question1 Types of Oscillators As widely cited, wave generators are of signal importance in electronics. Modern generators often use different circuits generating outputs such as trapezoidal, squire, saw tooth, and Sinusoidal wave shapes. One such type of a wave generator is referred to as an oscillator. In this context, an oscillator is regarded as the amplifier, which generates an input signal of its own. Oscillators can be classified basing on the wave shapes they produce, as well as the requirements for them to produce such oscillations. Generally, there are two categories of oscillators: Sinusoidal, and none-sinusoidal. Sinusoidal oscillators are characterized by producing a sine wave output signal. Such a signal output is known basically to have an amplitude that is constant but with no frequency variations. In reality something lower than this is normally obtained. The level to which the real situation is realized is dependent on factors such as the amplifier class, characteristics of amplifier, stability of frequency, as well as stability of amplitude. Generators identified as being sine wave give out signals that range from low audio frequency to radio and microwave frequencies often considered as ultrahigh. It is worth noting that there is a significant number of generators have low frequency and utilize capacitors and resistors in establishing their frequency networks. Such generators are known as RC oscillators and they are applicable in ranges of audio frequency. There are other forms of sine-wave generators that utilize capacitors and inductors in the determination of the frequency. These categories of generators are referred to as the LC oscillators. They do use circuit tanks for high radio frequencies. These generators are not suited to be used as purely oscillators of low-frequencies as the capacitors and inductors would have a larger size, be costly to manufacture and heavy. The third category of generator is known as crystal controlled oscillator. This oscillator gives out frequency that is excellent and is applied in middle audio range and radio range frequency. Nonsinuisoidal Oscillators, on the other hand, are known to give out waveforms, which are of the shape of rectangular, trigger, square, trapezoidal and saw tooth. Their outputs are characterized by a change that is sudden and relaxed making them is identified as relaxation oscillators. These oscillators have a signal frequency governed by the discharge or charge time of a resistor with a capacitor in series. Some types have inductors which influence the frequency output. Similar to the sinusoidal oscillators all the LC and RC networks are useful in determining the oscillation frequency. In this type, oscillators that are non sinusoidal are blocking oscillator, multivibrators, trapezoidal and saw-tooth generators. Generally, an oscillator is an amplifier that gives out itself in form of feedback with a signal in the input. This is a device that is non-rotating in producing current that is alternating, the frequency output that is established by the device traits. The primary role for the oscillator is to give out waveforms at a peak that is constant and frequency that is specific to maintain the waveforms in certain frequency and amplitude limits. The oscillator has to give out amplification. In this respect, signal power amplification happens to the output from input. For an oscillator, an output portion is fed back to sustain the input. This means that plenty of power needs to be feedback towards the input circuit for the self driving. Response to Task 2 Question 2. The circuit conditions and the methods used to achieve sinusoidal oscillation An electronic oscillator is can be defined as an electronic circuit that often produce oscillating, repetitive, and electronic signal, either a square wave or a sine wave. Most oscillators work by converting direct current from a given power supply to an equivalent alternating current signal. Most electronic devices make use of oscillating circuits. Example include signals that are generated by oscillators and these include signals broadcasted by clock signals, television and radio and transmitters, which function by regulating quartz and computers along with sounds that are produced by electronic video games and beepers. There are basic conditions and methods that can be used to achieve a sinusoidal oscillation. Notably, there are three essential rules that should be met for any circuit to be used as an oscillator circuit. First, the circuit must contain a tank circuit for producing damped oscillations. Second, the given circuit must have an amplifier and the gain for the amplifier must be greater than unity. Last, but not least, the circuit must provide a positive feedback and a feedback circuit. The figure below shows an example of an oscillator circuit. Response to Task 2 Question 4 a) Provided that in a Wien-Bridge Oscillator, the Resonance frequency is often found using the formula Fr = 1/2RCπ This implies that with C being made the subject of the formula, the value of the capacitor is given from the formula C= 1/2RFrπ = 1/188495.56= 5.30516*10-3F From this, it is clear that the value of capacitor needed = 5.30516*10-3F b) Close loop gain and feedback factor Let the amplifier voltage gain be A while the feedback attenuation be B Given that the closed loop gain (X) is equal to A / [ 1 + (A x B )] and the feedback factor being Y = A / X C) In order to find the output voltage, the formular Vout = Vin (1 + R2/R1)= 150mV/45O shall be of use and this implies, on substitution (Output voltage) Vout = (1+ 200/200)* 150mV/45O= 2*150mV/45O= 300mv/45O. Thus the output voltage for the oscillating circuit with the input voltage becomes 150mV/45 is 300mv/45O Response to Task 2 Question 5 Explain the advantages of crystal-controlled oscillator circuits Crystal oscillators, commonly referred to as XOs, are dependent upon a piezoelectric quartz crystal for resonance. Piezoelectric quartz is used in determining the frequency at which the oscillators oscillate. In this regard, crystals are cut having precise dimensions purposely to make them oscillate at certain specific frequencies. Following superior frequency selectivity of a crystal, the frequency of the oscillator is quite accurate and stable. Crystal oscillators find their application in electronic clocks, as well as in other applications, in which extreme accuracy is required. The crystal oscillators, when using capacitive and inductive circuits, are more accurate, and they also tend to oscillate at a much higher frequency compared to what can be achieved with a turned circuit design. This clearly means that a crystal oscillator utilizes the mechanical resonance of the vibrating crystal for piezoelectric material in creating an electric signal with a certain frequency that is very precise (Humphrey, 2004). Such a frequency is used in keeping track of time for purpose of providing a stable clock signal in digital integrated circuits, as well as stabilizing frequencies in receivers and radio transmitters. The oscillator circuits that incorporate piezoelectric materials are called crystal oscillators. Clearly, unlike other oscillating circuits, a crystal oscillator has a mechanical resonance of the vibrating crystal that it uses in creating an electric signal with a certain frequency that is very precise. Arguably, the use of crystals in crystal circuits makes them advantageous. It has also been noted that cutting properly the crystal of quartz and mounting it properly makes it possible to distort an electric field through applying some voltage on an electrode on a crystal. This is the property that is commonly referred to as piezoelectricity. Removing the field enables quartz to generate an electric field when turning to the previous shape, thereby generating a voltage. This way, a quartz crystal behaves in a similar way to the circuit consisting of a resistor, a capacitor and an inductor with precise resonance frequency. Moreover, the elasticity constant of quartz along with the property to change the size such that frequency dependence on temperature becomes low is an advantage when used in crystal oscillator circuits. The definite characteristic depends on the vibration modes, as well as the angle by which the cutting of quartz is done relative to the crystal graphic axes. This implies that the resonance frequency of such a plate that is depended upon its size does not change, either. Because of this property of the quartz material, the quartz clock, oscillator or filter is meant to remain accurate. The flexibility of quartz makes it possible for quartz oscillator to be mounted in some temperature controlled container often referred to as a crystal oven. It can, as well be mounted on a shock absorber for purposes of preventing some perturbation caused by external mechanical vibrations. It is also argued that a crystal oscillator circuit has the ability of sustaining oscillations. In this specific case it can be used to take some voltage signal from a quartz resonator, hence, amplifying it, and then feeding it. For other oscillator circuits, for instance the RC oscillators, research indicates that such oscillator circuits have a network of resistors and capacitors serving as filters (Bosco, 1999). This means that majority of the RC circuits serve the purpose of generating lower frequency for instance in audio range. The most common types of the RC circuits include the Wien Bridge and the phase shift oscillators. Research as well indicates that LC oscillator circuits are characterized by turned circuits also called tank circuits, which are used as filters. They consist of a capacitor and inductor connected together. For these circuits to be effective, charge tends to flow back and forth between the plates of a capacitor and an inductor. It is because of this property that turned circuits can be used for storing electric energy that oscillates at its resonance frequency. As widely noted, losses in tank circuits are relatively small. However, the amplifier help in compensating for such losses through supplying the much needed power for the required output signal. The LC oscillator circuits are commonly used in radio frequencies, especially where a tuneable frequency source is needed. References. Ellinger, F. (2008). The Radio Frequency Integrated Circuit and Technology. New York: John Wiley and sons. Bosco, B. (1999). The Behavior Experimental Analysis. American Scientist, 45(4), 343-371 Humphrey, M. (2004). The Fifth Discipline: The Art and Practice of the Learning Organization. New York: Doubleday Read More