Physics EEI

Contents
Introduction 4

Astable Multivibrators 4

Overview of the 555 Timer 5

Integrated Circuit 5

Semiconductor material 7

Current and Resistance 9

Potentiometer 10

Calculation of the Voltages 11

Transistors 11

Light Emitting Diode (LED) 14

Capacitance 14

555 Timer Operations 15

Operation in the Astable State 17

Aim, Hypothesis, and Calculations 18

Aim 18

Hypothesis 19

Materials 20

Method 20

Variables 21

Independent variable 21

Dependant variable 22

Controlled variable 22

Results 23

Table 1: Theoretical Values of varying Resistor R1 23

Table 2: Experimental values varying resistor 1 (R1) 24

Table 3: Theoretical values varying resistor 2 (R2) 25

Table 4: Experimental values varying resistor 2 (R2) 26

Data Analysis and Discussion of Trends Using Appropriate Pot 1 27

Trend 27

Matching the Frequencies of the Chosen Songs 29

Overall Results 30

Discussion 31

Conclusion 38

References 40

Appendix 43

Error Calculations 43

The extra resistor from the wires connecting the components in the circuit 43

The effect of temperature on the resistivity of the fixed resistors in the circuit 43

Calculations of best pot 44

Choice of Resistor and Pot 44

Calculation of Frequency Ranges 44

Introduction

Shaping and generation of waves is done using electronic circuits known as multivibrators. These circuits produce outputs that can be characterized as either stable or unstable in state. This project will discuss how a 555 Timer IC chip is applied in an Astable multivibrator when it operates in its astable state.

Astable Multivibrators

According to Wayne Storr (2013), Astable multivibrators do not have any states that are stable. That means that their modes switch from one state to another even when no external input is applied to them. Their unstable nature makes them susceptible to changes from minor external effects during their operation. They produce free oscillation that lead to the formation of rectangular waveforms(Daenotes,2015). Some of the primary components of these types of electronic circuits include ICs and transistors. Other components such as timers and operational amplifiers are also included in the construction of the Astable Multivibrators.

Overview of the 555 Timer

The 555 IC finds many applications in electronics because it is one of the easiest timers to use. Additionally, it is cost effective and available in many electronics shops. Sometimes, two independent ICs of the 555 timers may be contained in a single package called a dual version known as the 556 IC.

This circuit is made of several components. Each of these components is discussed here below in order to create a better understanding of the circuit shown above.

Integrated Circuit

It is usually abbreviated as IC. They are sometimes referred to as a microchip or a chip. It is a form of a wafer made of a semiconductor material such as silicon. It provides a basis for the fabrication of elements such as capacitors, resistors and transistors in large numbers. Additionally, they play various roles in the component where they are installed and fabricated. For instance, they can be used in the place of counters, amplifiers, computer memory, oscillators, microprocessors, or as timers. The intended application determines the classification of the IC into linear or digital integrated circuits. Overall, ICs require a low voltage of 15V to operate efficiently (Taylor, 2013).

Figure 1 – A diagrammatic representation of the 555 timer

According to Britannica (2014), the continuous output of the linear IC is always variable, and is determined by the levels of the input signals. For this reason, the output signal and the level of the input signal have a linear relationship. The graph of the instantaneous out signal level against the instantaneous input signal produces a straight line with a positive gradient. In most cases, this class of ICs uses operational amplifiers to aid in the functioning of audio-frequency and radio-frequency amplifiers.

On the other hand, digital ICs produce discontinuous amplitudes corresponding to the analog input signals. That is to mean that they function at particular states and levels of the signals. They find wide applications in frequency counters, computers, modems, and computer networks. Notably, they make use of logic gates to establish two states where they operate best. They are said to be low when at logic 0 and high when at logic 1 (Nave,2015).

The 555 Timer:

BBC (2015) argues that there are various types of the 555 timers depending on the number of pins. For instance, there are some that have 8 pins while others have 14 pins. These are shown in the diagrams below.

[pic]

The following illustration shows how the chip of the 555 timer is drawn in circuit diagrams. The pins differ from that of the actual. The arrangement eases the recognition of the function done by each of the pins. It also eases the sketching and drawing of the circuit diagrams.

[pic]

The timer applies digital and analogue techniques in its operation. However, its output is purely digital (Surtell.M, 2010). At various instances, the output can be low (0 V), or high state (Voltage of supply power).

Semiconductor material

There are three types of materials. These are conductors, insulators and semiconductors. Every material is classified in either of these classes depending on its electrical conductivity levels and properties (R.Nave,2015). These three types differ in electrical conductivity and properties due to the band theory. The band theory consists of three bands. These include the valence, conduction and the forbidden bands (B.Van Zeghbroeck,2011). Electrons move freely within the conduction band. The valence band is the highest energy level and contains valence electrons. On the other hand, the forbidden band is found between the valence and conduction bands. Its role is to prevent the flow of electrons between the two bands.

Conductors are materials allow the flow of electrons within their structures. The conduction band has a low resistance and overlaps with the valence band. In insulators, the flow of electrons is restricted because the valence and conduction bands are separated by extremely wide gaps. The band gap has such a high resistance that it cannot permit electrons to cross to either side of it. On the other hand, semiconductors allow the flow electrons between the conduction and valence bands under particular conditions. Unlike in insulators, the energy gap between the two bands is not wide enough to prevent electron flow (Physics Classroom,2015). As such, electrons can cross the forbidden band under the suitable conditions. There are two types of semiconductors. These are the intrinsic and extrinsic semiconductors(GITAM,2015). Intrinsic refers to materials that do not contain any impurities in their structures. As such, the number of free electrons available is equivalent to the number of holes created. Extrinsic semiconductors are also referred to as doped semiconductors. They are said to be doped because some impurities are added to the materials to improve their electrical conductivity and properties.

Electrons create holes when they move from the conduction to the valence band across the forbidden band. Normally, holes contain a positive charge. The next electron leaves its position to occupy the hole created by the electron that moves. This way, an electric current is established when subsequent electrons move to occupy holes.

Doping is done using materials known as dopants. These dopants can be used to create either N Type or P type semiconductors. N Type semiconductors contain impurities in the form of phosphorous or arsenic as in the case of intrinsic materials. Arsenic and phosphorous are examples of pentavalent dopants. On the other hand, P Type semiconductors contain trivalent dopants such as gallium and boron. N Type semiconductors contain more electrons than holes. For this reason, they have a negative charge. On the contrary, P Type semiconductors have more holes than electrons; hence they have a positive charge (N.Rave,2015).

Current and Resistance

Materials that allow current charge to flow through them are referred to as conductors. Current is the flow of electrons, the particles in an atom that carry the negative charge. This flow is sometimes limited by the resistance present in some materials. The quantity of resistance in a material can be obtained using the following formula.

R=ρ[pic].

In this equation, L represents the length, A is the area of the cross section, ρ is the resistivity to the current flow, and R is the resistance. Resistance is expressed in units known as Ohms (Ω). The heat generated by the flow of electrons affects the resistance of the material. Some materials have a positive temperature coefficient. Their resistance increases when the surrounding temperature is increased. However, resistance changes as temperature varies.

Resistance depends on the resistivity of the temperature (Rt), resistivity of absolute temperature (R0), temperature (T), reference temperature (T0), and the coefficient of resistivity of temperature. These factors are connected by the following equation. According to Boser (2009), the equation is also used to determine the resistance of a material at any given instance provided the values are known.

Rt =R0 {1+α (T-T0)}

Materials that have a significant amount of resistance are known as resistors. It has two terminals and offers significant resistance to the flow of current. Additionally, current in an electric circuit is usually driven by voltage. In this project, a voltage of 9V will be used. It will be drawn from a battery and used to convert chemical energy to electrical energy. This conversion will result in the production of a potential difference across the terminals of the battery. The voltage difference across the terminals drives the current against the resistance. According to Ohm’s law, the amount of the voltage is equivalent to the product of the current and the resistance values (Q=IT). Mathematically, this can be expressed as V=IR. From this equation, the value of the resistance can be evaluated if it is not given. Given the values of the voltage and current, R=V/I. It is thus expressed as a ratio of the current and voltage. It is also worth noting that some power is dissipated during this current flow. Nave (2015) shows that the amount of the power dissipated can be obtained using the formula P=VI=V (V/R)=V2/R.

Potentiometer

Sometimes it is necessary to vary the resistance of an element. This is achieved with the use of a variable resistor that consists of three terminals. A wiper is connected to one of the three terminals and then slided along the material that is resistive. An example of a device used to vary resitsnce is the potentiometer. It is used to vary the voltage accordingly. It is sometimes used togather with a rheostat that varies the current flow. In this experiment, a resistor will be used to adjust the voltage levels in the voltage divider network used. This network will be used to split the large voltages into smaller amounts. It consists of reistors connected in series. The output voltage passing through every resistor is used as the input to the other components in the network.

Calculation of the Voltages

The sum of all currents across the resistors is obtained. The voltage is then divided by this sum. Ohm’s law is the applied to calculate the value of the voltage. Ohm’s Law states that voltage is a product of the current and resistance in the network or circuit. Alternatively, Facstaff (2010) argues that the value of the resistance of every resistor can be expressed as a percentage of the total resistance. The ratio is then applied by the voltage applied. Mathematically, this can be shown as follows.

[pic]

The 555 Timer used in this experiment will contain three resistors whereby each has a resistance value of 5KΩ. From calculation, each resistor will have a voltage drop that is one third of the total supply voltage. Therefore, the voltage drop across each resistor will be one-third of the supply voltage. For instance, if the voltage supply is 9V, the potential drop after the first resistor is 6V and 3V after the third resistor.

Transistors

Transistors are semiconductor devices that are used for the amplification and switching of signals, as well as electrical power. It usually has a minimum of three terminals that are connected to the external circuits. They are made of semiconductor materials. Currents in the terminals are changed when voltage or current flows through any two of the terminals of the device. Amplification of signals is possible because the output power exceeds the input (controlling) power. Most of these transistors are usually integrated in the IC packages or sometimes packaged as an individual/single chip.

According to Carlson (2013), amplification and switching are the primary functions of transistors. In the case of a 555 Timer, they are used as a switch in creating a discharge path to the circuit network. It has n-type and p-types. There are two possible combinations that can be used. Firstly, two n-type semiconductors and one p-type semiconductor can be used. Secondly, two p-type and one n-type semiconductors can be used. The field between these two transistor fields is made of a material that is slightly doped. It forms the base between the emitter and collector. In npn transistor, the arrow of the emitter points outwards. That is in the case of the 555 Circuit shown.

Application of a low voltage to the base drives the transistor to the cut-off region. That is the region where the transistor is in its off mode and acts as an open switch. The base current (Ib) goes to as low as zero while the junction between the emitter and the base is reverse biased. Due to this, the collector current is zero (Ic=0). Saturation occurs when the voltage applied is high. The transistor is in its ON mode and acts as a closed switch during this state. Forward biasing takes place at the base-emitter junction and the collector current is at its peaks. Current flow to the collector is maximal. It also allows maximum current to pass through it, causing the forward bias at the junction. It is for this reason that the on/off state of the transistor is controlled by its base. The transistor is said to be operating in either its saturation or cut-off mode when the output, Q̂, of the SR Flip-Flop in the 555 timer is a digital output. This is shown in the following diagram.

[pic]

The following diagrams show transistors. They also show their three terminals and the two types; npn and pnp types.

[pic]

[pic]

Light Emitting Diode (LED)

Diodes are electronic devices in which current flows in one direction and blocks flow in the reverse direction. It contains p and n type semiconductors joined. These two semiconductors meet at an area called a junction. Forward bias occurs when the negative terminal of the battery is connected to the cathode and the positive terminal to the anode. Current repels holes and pushes electrons till they cross the junction, allowing current flow. According to Honsbery & Bowden (2002), energy is released in the form of photons when the threshold voltage of the material is exceeded. These photons are characterized by low frequencies and long wavelengths, hence falling out of the visible spectrum. The light is visible since a semiconductor has a high frequency. For this reason, forward bias is required for LEDs to emit light. No current flows during reverse biasing since the electrons and holes are driven away from the junction (J.Lesurf, 2005).

Capacitance

Capacitance is stored by capacitors in the form of energy and charge. Capacitors are made of two plates that sandwich a dielectric material that acts as an insulator. Electric charge builds up on the plates when the capacitor is connected to a battery. The charge acquired is equivalent to that drawn from the battery but of the opposite polarity. This charge is called capacitance and it is measured in farad (F). According to Nave (2015), resistance increases the rate of discharging and charging. For this reason, resistance affects the time taken to charge or discharge a capacitor. This time is referred to as the time constant, τ, and it is the rate at which capacitors discharge. Time constant, resistance and capacitance are related through τ = RC. Nave (2015) also argues that the voltage of a capacitor can be expressed as a function of time taken to charge it. This is expressed by[pic]. The rate of discharging is estimated through [pic]. In this case, [pic] is the capacitor’s initial voltage and e=base natural for algorithms=2.718 (Penn Engineering, 2013). When the value of the base natural voltage is increased, the transistor is on and allows current to pass. Lowering the voltage value of base natural voltage switches the circuit off. The timer is LOW when the input is inversed. Hence, the output goes off.

555 Timer Operations

Figure 1 shows a voltage divider network in which three resistors of 5KΩ are connected in series. That means that each resistor experiences a voltage drop of one-third of Vcc since they are equal. A reference voltage is formed by the three resistors at one input of each of the comparators. According to Texas Instruments (2015), comparator 1 has two-thirds of Vcc while comparator 2 receives one-third of Vcc. the input S of the flip flop is fed by comparator 2 when the trigger input voltage of pin 2 falls below the reference voltage. At that instance, comparator 2 has a HIGH output. The output (Q̂) of the flip-flop goes LOW while the input (Q) is HIGH. The output of comparator 1 is HIGH when the threshold input (pin 6) voltage goes above the reference voltage. Roberts (2001) argues that the Q̂ output is inverted, changed to a LOW, and the output of the timer is LOW.

Also, the Flip-Flop’s output Q̂ is connected to transistor’s base. When Q̂ is HIGH, the transistor is in the state of saturation. When the Flip-Flop’s output Q̂ is LOW, the transistor is in the state of cutoff (Nave, 2015).

The outputs sequence of the 555 timer can be shown in the form of a table as below:

|Voltage at |Comparator 1 Output |Comparator 2 Output |Flip-Flop Output|Flip-Flop Output|Transistor state Q1 |
|Pin 2 and 6 (V2-6) |(R) |(S) |Q |Q̂ | |
|<1/3 Vcc |Low |High |High |Low |OFF |
|1/3Vcc<V2-6<2/3Vcc |Low |Low |Stay |stay |Stay |
|>2/3Vcc |High |Low |Low |High |ON |

By using resistors and capacitors to produce an RC time constant, the circuit in Figure 1 can be configured to design an Astable multivibrator.

Operation in the Astable State

|Voltage |Comp 1 Output |Comp 2 Output |
|V2-6 | | |
|555 timer chip |1 |Average size (very small) |
|Breadboard |1 |Average size (relatively small) |
|Capacitor |1 |10[pic]F (Minimum value of the Capacitor. |
| | |Kept constant) |
|Resistor |2 |50K[pic] and 500K[pic] |
|Multimeter |1 |Average size |
|Potentiometer |4 |A500k, A50K, B500K, B50K |
|9V Battery |1 |9 volts |
|9V Battery Connector |1 |Average size |
|Sparkvue cables |1 |Average size |
|LED (Yellow) |1 |Average size (small) |
|Wires |Multiple |Different sizes ranging from 2cm – 6cm |
|Laptop |1 |Any |

Method

i. The 555 oscillator circuit was set up in its astable mode with the circuit components (555 timer, resistors, capacitors, wires, etc) placed in certain positions in the breadboard. ii. Once the components were placed together and the circuit was created, the original resistance (R1 and R2) and the capacitance (C) was recorded. iii. The period and frequency of the circuit was then measured using a computer program, Sparkview and calculations. iv. Three different tests were conducted; keeping the first resistor (R1) and capacitance (C) constant and varying the second resistor (R2), keeping the second resistor (R2) and capacitance (C) constant and varying the first resistor (R1) and keeping both resistors (R1 and R2) constant whilst varying the capacitance (C). v. The resistance of R1 and R2 was varied using an A500k potentiometer. vi. Using SparkView and further calculations, the period and frequency of the circuit was measured. Once these factors were tested, based on observations and general knowledge, the resistance of R2 was varied in order to achieve the flashing LED in sync with three different songs with frequencies of 1.6Hz, 2.0Hz and 2.4Hz (96bpm, 120bpm and 144bpm). The resistance value needed for this to occur was recorded.
Note: Before the experimental phase took place, theoretical calculations were conducted which provided values for what should/is expected to occur. Based on the experimental values gathered, comparisons and conclusions were drawn.

Please refer to the discussion for the extended dissertation. Please refer to the results section for the data compiled and the values of the constant and varied factors. Finally, please refer to the Journal for further detail.

Variables

There are three types of variables used in this experiment. They are independent variables, dependent variables, and the controlled variable.

Independent variable

The independent variables used in this investigation were the capacitance and the resistance of capacitor and potentiometer used, respectively. These values of the two variables were obtained from the external Resistor-Capacitor network the 555 Timer Chip (the astable multivibrator used).

Dependant variable

The dependent variable in the practical was the frequency of the flash produced by the LED. It was dependent because its value depended entirely on the values of the capacitance and resistance as shown earlier by the following equation.

[pic]

Controlled variable

The controlled variables refer to the variables that determine the overall output and results obtained. They include the resistors connected in series in the circuit, the supply voltage in the circuit, the red LED used, connecting wires that run through the chip, and the how the 555 Timer Chip was positioned. All these variables had a direct effect on the accuracy and nature of results and forms (exponential or liners) obtained.

Results

Table 1: Theoretical Values of varying Resistor R1

P1 (Ohms) |P2 (Ohms) |R1 Total (Ohms) |R2 Total (Ohms) |Avg On Time (Sec) |Avg Off Time (Sec) |Total Period (Sec) |BPM |Frequency (Hertz) | |0 |0 |22000 |10000 |0.222 |0.069 |0.291 |206.18 |3.40 | |110 |0 |22110 |10000 |0.223 |0.069 |0.292 |205.48 |3.39 | |9800 |0 |31800 |10000 |0.290 |0.069 |0.359 |167.13 |2.76 | |21000 |0 |43000 |10000 |0.367 |0.069 |0.437 |137.30 |2.27 | |27400 |0 |49400 |10000 |0.412 |0.069 |0.481 |124.74 |2.06 | |37200 |0 |59200 |10000 |0.480 |0.069 |0.549 |109.29 |1.80 | |41300 |0 |63300 |10000 |0.508 |0.069 |0.577 |103.99 |1.71 | |47100 |0 |69100 |10000 |0.548 |0.069 |0.618 |97.09 |1.60 | |49000 |0 |71000 |10000 |0.561 |0.069 |0.631 |95.09 |1.57 | |100000 |0 |122000 |10000 |0.915 |0.069 |0.984 |60.98 |1.00 | |220000 |0 |242000 |10000 |1.747 |0.069 |1.816 |33.04 |0.55 | |340000 |0 |362000 |10000 |2.579 |0.069 |2.648 |22.66 |0.37 | |420000 |0 |442000 |10000 |3.133 |0.069 |3.202 |18.74 |0.31 | |500000 |0 |522000 |10000 |3.757 |0.069 |3.826 |15.68 |0.26 | |

Table 2: Experimental values varying resistor 1 (R1)

P1 (ohms) |P2 (ohms) |R1 Total (ohms) |R2 Total (ohms) |Avg On Time (sec) |Avg Off Time (sec) |Total Period (sec) |BPM |Frequency (Hertz) | |0 |0 |22000 |10000 |0.215 |0.072 |0.287 |209.06 |3.48 | |110 |0 |22110 |10000 |0.218 |0.072 |0.290 |206.90 |3.45 | |9800 |0 |31800 |10000 |0.290 |0.072 |0.362 |165.74 |2.76 | |21000 |0 |43000 |10000 |0.363 |0.072 |0.435 |137.93 |2.30 | |27400 |0 |49400 |10000 |0.418 |0.072 |0.490 |122.45 |2.04 | |37200 |0 |59200 |10000 |0.481 |0.072 |0.553 |108.50 |1.81 | |41300 |0 |63300 |10000 |0.522 |0.072 |0.594 |101.01 |1.68 | |47100 |0 |69100 |10000 |0.567 |0.072 |0.639 |93.90 |1.56 | |49000 |0 |71000 |10000 |0.585 |0.072 |0.657 |91.32 |1.52 | |100000 |0 |122000 |10000 |0.984 |0.072 |1.056 |56.82 |0.95 | |220000 |0 |242000 |10000 |2.159 |0.072 |2.231 |26.89 |0.45 | |340000 |0 |362000 |10000 |3.462 |0.072 |3.568 |16.82 |0.28 | |420000 |0 |442000 |10000 |3.287 |0.072 |3.347 |17.93 |0.30 | |500000 |0 |522000 |10000 |4.391 |0.072 |4.459 |13.46 |0.22 | |

Table 3: Theoretical values varying resistor 2 (R2)

P1 (ohms) |P2 (ohms) |R1 Total (ohms) |R2 Total (ohms) |Avg On Time (sec) |Avg Off Time (sec) |Total Period |BPM |Frequency (Hertz) | |0 |0 |22000 |10000 |0.222 |0.069 |0.291 |206.18 |3.43 | |0 |246 |22000 |10246 |0.224 |0.071 |0.295 |203.39 |3.39 | |0 |6790 |22000 |16790 |0.269 |0.116 |0.385 |155.84 |2.60 | |0 |13630 |22000 |23630 |0.316 |0.164 |0.480 |125.00 |2.08 | |0 |20500 |22000 |30500 |0.364 |0.211 |0.575 |104.35 |1.74 | |0 |27800 |22000 |37800 |0.415 |0.262 |0.677 |88.63 |1.48 | |0 |39400 |22000 |49400 |0.495 |0.342 |0.837 |71.6 |1.19 | |0 |44000 |22000 |54000 |0.527 |0.374 |0.901 |66.59 |1.11 | |0 |49100 |22000 |59100 |0.562 |0.410 |0.972 |61.73 |1.03 | |0 |98700 |22000 |108700 |0.906 |0.753 |1.659 |36.17 |0.60 | |0 |229000 |22000 |239000 |1.809 |1.657 |3.466 |17.31 |0.29 | |0 |300000 |22000 |310000 |2.301 |2.149 |4.450 |13.48 |0.22 | |0 |400000 |22000 |410000 |3.001 |2.849 |5.850 |10.26 |0.18 | |0 |500000 |22000 |510000 |3.683 |3.535 |7.218 |8.31 |0.14 | |

Table 4: Experimental values varying resistor 2 (R2)

P1 (ohms) |P2 (ohms) |R1 Total (ohms) |R2 Total (ohms) |Avg On Time (sec) |Avg Off Time (sec) |Total Period |BPM |Frequency (Hertz) | |0 |0 |22000 |10000 |0.216 |0.071 |0.287 |209.06 |3.48 | |0 |246 |22000 |10246 |0.217 |0.072 |0.289 |207.61 |3.46 | |0 |6790 |22000 |16790 |0.265 |0.119 |0.384 |156.25 |2.60 | |0 |13630 |22000 |23630 |0.314 |0.159 |0.473 |126.85 |2.11 | |0 |20500 |22000 |30500 |0.363 |0.209 |0.572 |104.89 |1.75 | |0 |27800 |22000 |37800 |0.414 |0.263 |0.677 |88.63 |1.48 | |0 |39400 |22000 |49400 |0.506 |0.361 |0.867 |69.20 |1.15 | |0 |44000 |22000 |54000 |0.548 |0.388 |0.936 |64.10 |1.07 | |0 |49100 |22000 |59100 |0.591 |0.430 |1.021 |58.77 |0.98 | |0 |98700 |22000 |108700 |0.965 |0.768 |1.733 |34.62 |0.58 | |0 |229000 |22000 |239000 |1.833 |1.597 |3.430 |17.49 |0.29 | |0 |300000 |22000 |310000 |2.337 |2.063 |4.400 |13.64 |0.23 | |0 |400000 |22000 |410000 |3.121 |2.612 |5.733 |10.47 |0.17 | |0 |500000 |22000 |510000 |3.926 |3.341 |7.267 |8.26 |0.14 | |

Data Analysis and Discussion of Trends Using Appropriate Pot 1

[pic]
Figure 1: This shows how the theoretical and experimental values compare between Resistances R1 and R2.

Trend

An increase in the values of R1 and R2 causes an exponential decrease in the value of the frequency. The frequency does not decrease despite an increase in R1 and R2 resistance values. It also observed that there is a very close relationship between the theoretical and experimental values of resistances R1 and R2. The difference between the theoretical and experimental resistance value of R2 is less than 0.0054 ohms. That indicates a very high degree of accuracy in carrying out the experiment. The experimental data also shows that a resistance of 50K[pic] in R1 causes a frequency of approximately 0.92 Hz and 0.50 Hz in R2. However, the application of a resistance of 500k[pic] drops the frequency to levels of around 0.12 Hz in Resistor 1 and 0.065 Hz in Resistor 2. For this reason, it is evident that increasing the value of Resistor 1 causes a larger change in the frequency levels than altering the values of Resistor 2.
[pic]
Figure 2: A comparison of the relation of theoretical and experimental data between resistance and period of R1 and R2 variables. A comparison of how the theoretical and experimental data between resistance and period of R1 and R2 variables relate is shown in the figure above. From the graph, it is evident that an increase in the values of resistances R1 and R2 causes a linear increase in the period. However, increasing R and R2 does not cause similar increments in the values of the period. It also shows a very close relationship between the theoretical and experimental values of R1 and R2. For instance, the difference between the two values of R2 is less than 0.0033 ohms. That indicates that the experiment was carried out accurately and with a great trend of precision. The experimental data shows that applying a resistance of 50K[pic] at both R1 and R2 causes a period of approximately 1.078sec and 1.99sec in R1 and R2 respectively. However, a load of resistance 500k[pic] on the two variables increases the period to approximately 7.7sec and 15.26sec in r and R2 respectively. These results show that increasing R2 has a greater effect on the period than an increase on the value of resistor R1.

Matching the Frequencies of the Chosen Songs

[pic]
Figure 3: Comparison of the relation between theoretical and experimental values for R2 required to match the frequency of each of the chosen songs A, B, and C. The experimental values were measured and recorded during the experiment. This graph shows how the theoretical and experimental values of R2 required to match the frequencies of the songs A, B, and C compare. In this experiment, the value of the capacitance C was kept constant throughout the practical. The graph shows that an increase in the value of the resistance if resistor R2 causes an exponential decrease in the value of the frequency. The values of the theoretical resistances of R2 showed a lower frequency than that of the three chosen songs represented by the blue dots. Therefore, the experimental values of the selected songs are less than the actual, theoretical values. The value of the resistance R2 must thus be lowered ion order to match the required frequencies of each of the three songs chosen for the practical. An estimation and calculation of the difference between the experimental and theoretical values of R2 showed that it varies from approximately 100[pic] to 240[pic]. Figure 1 was also used to show that an increase in the resistance causes a decrease in the value of the frequency of the songs used in the practical. An accurate conclusion that can be made in this case is that there are present additional resistances within the circuit configuration. These additional resistances combine with the value of resistor R2 to increase resistance, lowering the frequency to lower levels than those of the selected songs.

Overall Results

The results obtained from the experiment show that increasing the resistance values of R1 and R2 causes an exponential decrease in the value of the frequency of the circuit. Additionally, it was observed that increasing the values of resistors R1 and R2 causes the period to increase linearly. These arguments are supported by the data represented in the graphs shown above. However, the proportion of the increments in the period and frequency of the circuits due to increase or decrease in the resistance values of R1 and R2 are not similar. Another notable detail is that four potentiometers were used in the practical and the capacitance was kept constant throughout the experiment. An error analysis of the results showed that the values obtained for R1 and R2 were accurate when compared to the theoretical values. It was also found that the value obtained for R2 was lower than the practical value required to match the frequency of each of the chosen three songs. This was accounted for by the presence of additional resistance in the circuit. Possible sources of extra resistance in the network include the generation of heat during the practical.

Discussion

This practical was carried out to determine how varying the resistances R1 and R2 affects the frequency and period of a circuit. In this case, an astable multivibrator with an external RC network was used. The hypothesis developed stated that increasing the resistor values of the two resistances caused varied exponential decrease in the frequency. Varying R1 had a greater effect on the frequency while varying R2 affected the period significantly. The period increased linearly since it is an inverse of the frequency in the circuit. However, the value of the capacitance was held constant throughout the experiment.

The effects of varying resistances R1 and R2 can be analyzed by considering the frequency formula. An inspection of the formula shows that increasing the values of R1 and R2 decreases the frequency exponentially and increases the period linearly. These changes occur even when the capacitance is kept constant, as was the case in this practical. An analysis of the results gathered and presented showed that they were in support of the hypothesis that had been set.

The frequency and period change depend on the value of the resistors and capacitor. For this reason, that increasing the components in an RC network (both resistors and capacitor) would result in an exponential decrease in frequency and linear increase in the period of the circuit however the increments. However, varying the resistance values of R and R2 had different magnitudes of effects on the frequency and periods of the current in the circuit of the Circuit network. It was also noted that there was extra resistance in the circuit. The total resistance value in the circuit was higher than what could be accounted for by the resistance accounted for by the value supplied by the two resistors, R1 and R2. This extra resistance resulted from increased friction in the connecting wires during the functioning and operation of the multivibrators.

The theoretical and experimental values of R2 required to match the frequencies of the three songs were compared. In this experiment, the value of the capacitance C was kept constant throughout the practical. The graph plotted using skills in excel showed that an increase in the value of the resistance if resistor R2 causes an exponential decrease in the value of the frequency. The values of the theoretical resistances of R2 showed a lower frequency than that of the three chosen songs represented by the blue dots. Therefore, the experimental values of the selected songs are less than the actual, theoretical values. These values were measured and recorded during the practical. The value of the resistance R2 must thus be lowered ion order to match the required frequencies of each of the three songs chosen for the practical. An estimation and calculation of the difference between the experimental and theoretical values of R2 showed that it varies from approximately 100[pic] to 240[pic].

Figure 1 was also used to show that an increase in the resistance causes a decrease in the value of the frequency of the songs used in the practical. An accurate conclusion that can be made in this case is that there are present additional resistances within the circuit configuration. These additional resistances combine with the value of resistor R2 to increase resistance, lowering the frequency to lower levels than those of the selected songs.

The results obtained from the experiment show that increasing the resistance values of R1 and R2 causes an exponential decrease in the value of the frequency of the circuit. Additionally, it was observed that increasing the values of resistors R1 and R2 causes the period to increase linearly. These arguments are supported by the data represented in the graphs shown above. However, the proportion of the increments in the period and frequency of the circuits due to increase or decrease in the resistance values of R1 and R2 are not similar.

Another notable is that two resistors were used in the practical. Additionally, the capacitance was kept constant throughout the experiment. An error analysis of the results showed that the values obtained for R1 and R2 were accurate when compared to the theoretical values. It was also found that the value obtained for R2 was lower than the practical value required to match the frequency of each of the chosen three songs. This was accounted for by the presence of additional resistance in the circuit. Possible sources of extra resistance in the network include the generation of heat during the practical.

The three songs selected for use in this exercise were labelled as Song A, Song B, and Song C. Theirs beats per minutes were 80, 112, and 158 for songs A, B, and C respectively. These beats corresponded to frequencies of 1.33 Hz (Song A), 1.86 Hz (Song B), and 2.63Hz (Song C).

Theoretical calculations were conducted in order to determine the exact resistance expected for R2, keeping R1 fixed at 10K[pic] and the C fixed at 22[pic]F, in order to get an exact frequency of each chosen song (1.33Hz, 1.86Hz and 2.63Hz). Two experiments were conducted; setting the resistance of R2 (with the use of an A500k potentiometer) to the theoretical resistance expected to achieve the same frequency of the chosen songs. The second experiment was varying R2 to attain a frequency as close as to the frequency of the chosen songs as possible. From the results attained, comparisons and relations were identified to determine justified reasons for the outcome (theoretical vs. experimental).

It can be noted from Figure 3 that as the resistance of R2 increases, the frequency decreases in an exponential form for both theoretical and experimental values. The theoretical resistance of R2 resulted in a lower frequency than the chosen songs whereas in order to match the frequency of the song, the resistance of R2 (experimental value) had to be decreased. The difference between the theoretical value for R2 to match the frequency of the songs and the actual resistance value required were 0.1k[pic], 0.14k[pic] and 0.24k[pic] respectively for the frequencies of 1.33Hz, 1.86Hz and 2.63Hz, showing that exponential trend. The theoretical R2 values for the frequencies of the song (15.31k[pic] for 1.6Hz, 11.23k[pic] for 2.0Hz and 8.53k[pic] for 1.6Hz) attained experimental frequencies of 1.5813Hz, 1.9697Hz and 2.3586Hz respectively. The variation between the theoretical and experimental frequency values range from approximately 0.0187Hz to 0.0414Hz as the resistance of R2 is decreased. This again shows an exponential relation between resistance and frequency. Based on the data, it can be established that the circuit maintained additional resistance which caused the theoretical values for R2 to result in lower frequencies than that of the chosen songs.

Some errors were incurred during the period of experimentation which led to slight inaccuracy in the data accumulated. The wires used in the circuit to create a pathway from a particular component to another (e.g. the wire connecting the LED to Pin 1) where not as short as possible. That extra unnecessary length increases the resistance in the circuit as can be seen from the equation R= ρ (L/A); when L (the length of the wire) increases, the resistivity also increases in proportion. The inaccuracy of equipment and rounding of values are other factor which potentially led to the inaccuracy in the results. The fixed resistors, capacitors, LED or the usb (used to work Sparkview) may have contributed to the inaccuracy in the results if the equipment used were internally damaged. Also the multimeter used to determine certain resistance values rounded the values to 1 decimal place again causing slight inaccuracy in resistivity readings. The temperature difference between the reference temperature (room temperature) and the temperature of the components (more importantly the resistors) has an effect on the resistivity. As the temperature of the component increase (further away from the reference temperature), the resistivity of the component increases. Therefore temperature is proportional to resistivity. From the equation Rt=R0{1+α(T-T0)}, it can be seen that if T (temperature of the component) is greater than T0 (reference temperature i.e. room temperature), it will result in an increase in the overall resistivity of the component and in this case, the fixed resistors are mostly affected. The capacitor used to vary the capacitance can have an error of +/- 20%. Finally the fixed resistors also maintained an error of +/- 5%.

There are ways of reducing the inaccuracy in the results if this investigation was to be completed again. During the setup of the components in the breadboard, the wires used to create a pathway from a particular component to the other should be cut to be as short as possible however still being capable of reaching the distance required. The reduction of the unnecessary length of the wire will reduce extra resistance in the circuit that affects the frequency and period of the circuit. The equipment used in the experimental phase such as the fixed resistors could be checked using a multimeter to find the precision in the resistivity value. Rounding of the resistivity readings could be performed to 2 decimal places to improve the accuracy of the results. The increase in temperature of the components which results in extra resistivity in the circuit is a factor which cannot be avoided or reduced without going to extremes. To improve the accuracy of the capacitance and resistance values of the capacitor and resistor, a simple solution is to conduct this experiment using more expensive and accurate equipment to enhance the error of the capacitor and resistor are as minimal as possible.

Although the increased resistivity in the circuit due to the extra length on the wires and the temperature of the components being greater than the reference temperature, the overall increased resistance in the circuit would have been quite minor for the range of resistors used. However the resistance error in the circuit is approximately a total of 1.3% and if this experiment was conducted again with larger fixed resistor values and the length of the wires were not shorten, using for example a 100k[pic] resistor would result in approximately 1300[pic] of extra resistance in the circuit simply from this one resistor. It is important to understand that all components in the circuit increase resistivity, even if that is not its main function in the circuit. As the temperature of each component increase, the resistivity in the circuit also increases in proportion. The resistors and capacitors would have be the largest contributing factor to the inaccuracy of the results due to the possible total error of +/- 25% of the actual resistance and capacitance values. The overall results received from the data were expected however with slight inaccuracy. The total error contributed from factors as mentioned above, from examination of the results section, establish minor error in this investigation and hence is discarded.

Resistance increases the rate of discharging and charging. For this reason, resistance affects the time taken to charge or discharge a capacitor. This time is referred to as the time constant, τ, and it is the rate at which capacitors discharge. Time constant, resistance and capacitance are related through τ = RC. Nave (2015) also argues that the voltage of a capacitor can be expressed as a function of time taken to charge it. This is expressed by[pic]. The rate of discharging is estimated through [pic]. In this case, [pic] is the capacitor’s initial voltage and e=base natural for algorithms=2.718 (Penn Engineering, 2013). When the value of the base natural voltage is increased, the transistor is on and allows current to pass. Lowering the voltage value of base natural voltage switches the circuit off. The timer is LOW when the input is inversed. Hence, the output goes off.

According to Honsbery & Bowden (2002), energy is released in the form of photons when the threshold voltage of the material is exceeded. These photons are characterized by low frequencies and long wavelengths, hence falling out of the visible spectrum. The light is visible since a semiconductor has a high frequency. For this reason, forward bias is required for LEDs to emit light. No current flows during reverse biasing since the electrons and holes are driven away from the junction (J.Lesurf, 2005). During the forward biasing, the semiconductor materials allow the flow of electrons; hence the flow of current is permitted. Therefore, current flow is allowed only during the forward biasing state of the semiconductor material. That is when the LED lights.

Conclusion

The practical was successful because it met the aims and purposes for the experiment. It was proven that increasing resistance in a circuit decreases the frequency and increases the period simultaneously. A frequency of 1.55 Hz is required in this experiment. This value is to be obtained using these values. The best pot that will best achieve this range is Pot 1. The potentiometer should be connected on resistor R1. The data collected during the experiment was used to compile this report on how an astable multivibrator circuit operates, as well as some of its functions. Engineers and designers can use the data, results, and materials suggested in this experiment to design and fabricate flashing lights at concerts, clubs and other entertainment events that require automatic flashing lights at certain intervals. These are some of the applications of astable multivibrators to the music industry.

The principles learnt in this experiment explain fundamental events such as how car manufacturers create indicators that flashes at certain time periods at constant intervals of on and off times when turning right or left. The skills gained can also be applied by the manufacturers that create road signals that consist of flashing lights to get the attention of people. Additional, it assists electricians because they need information on how resistors affect the frequency of lights (LED) in homes, buildings and many other different places.

However, the experimental design could be modified and new variables investigated in order to find other possible relationships and observations to further extend on this investigation. This would assist in carrying out further research on the operation of astable multivibrators, as well as the effect of varying resistance on the frequency and period in a circuit network. For instance, future investigators could use a wider range of different values of varied resistance and capacitance, different colored LED, different types of potentiometers, different temperature conditions, different wire lengths and a different type of multivibrator. The results obtained using these new parameters could be used to designer more advanced appliances that operate on the principle of the astable multivibrators.

References

1) Storr, W. (2013). Astable Multivibrator and Astable Oscillator Circuit. Basic Electronics Tutorials. Retrieved 27 August 2015, from http://www.electronics-tutorials.ws/waveforms/astable.html 2) Daenotes.com,. (2015). ASTABLE MULTIVIBRATOR. Retrieved 27 August 2015, from http://www.daenotes.com/electronics/digital-electronics/astable-multivibrators-working-construction-types 3) Taylor, C. (2013). Understanding Low-Power IC Design Techniques.Electronicdesign.com. Retrieved 27 August 2015, from http://electronicdesign.com/power/understanding-low-power-ic-design-techniques 4) Encyclopedia Britannica,. (2014).integrated circuit (IC) | electronics. Retrieved 27 August 2015, from http://www.britannica.com/technology/integrated-circuit 5) Hyperphysics.phy-astr.gsu.edu,. (2015).Integrated Circuits. Retrieved 27 August 2015, from http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/iccomp.html 6) Hyperphysics.phy-astr.gsu.edu,. (2015).Integrated Circuits. Retrieved 27 August 2015, from http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/iccomp.html 7) Bbc.co.uk,. (2015). BBC - GCSE Bitesize: Integrated circuits 1: 555 timer. Retrieved 27 August 2015, from http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/electronicsrev7.shtml 8) Suretell, M. (2010). The 555 Timer - Electronics in Meccano. Retrieved 27 August 2015, from http://www.eleinmec.com/article.asp?1
(9) Hyperphysics.phy-astr.gsu.edu,. (2015).Semiconductor Physics for Solid State Electronics. Retrieved 27 August 2015, from http://hyperphysics.phy-astr.gsu.edu/hbase/solids/sselcn.html
(10) B.Van Zeghbroeck (2011). Energy bands. Retrieved 27 August 2015, from http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_3.htm
(11) Nave.R (2015). Conductors and Insulators . Retrieved 27 August 2015, from http://www.physicsclassroom.com/class/estatics/Lesson-1/Conductors-and-Insulators
(12) Gitam.edu,. (2015). Contents. Retrieved 27 August 2015, from http://www.gitam.edu/eresource/Engg_Phys/semester_2/semicon/int_ext.htm
(13) Hyperphysics.phy-astr.gsu.edu,. (2015).Electric Power. Retrieved 27 August 2015, from http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepow.html
(14) https://www.eecs.berkeley.edu/~boser/courses/40/assignments/HW11.pdf 2011- reference properly
(15) Penn Engineering. (2013). Retrieved 27 August 2015, from http://www.seas.upenn.edu/~ese112/spring10/lectures/capacitors.pdf
Christiana Honsbergand Stuart Bowden (2002). Energy of Photon | PVEducation. Retrieved 27 August 2015, from http://www.pveducation.org/pvcdrom/properties-of-sunlight/energy-of-photon
(16) Jim Lesurf,. (2005). How a pn-junction diode works. Retrieved 27 August 2015, from https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/comp/passive/diode/pn_junc/pn_junc.htm
(17) Texas Instruments,. (2015).LM555 Timer. Retrieved 27 August 2015, from http://www.ti.com/lit/ds/symlink/lm555.pdf
(18) Nave.R 2015). Frequency and Period of a Wave . Retrieved 27 August 2015, from http://www.physicsclassroom.com/class/waves/Lesson-2/Frequency-and-Period-of-a-Wave

Appendix

Error Calculations

The extra resistor from the wires connecting the components in the circuit

R= ρ (L/A) where p of the copper wire = 1.68 x 10-4[pic]m and A of the wire = 5.2 x 10-4m2

Therefore R= {(1.68 x 10-4[pic]m) x L}/5.2 x 10-4m2)

Sub L = 2.5cm (0.025m), L = 5cm (0.05m), L = 7.5cm (0.075m) and L = 10cm (0.1m) to find the extra resistance in the circuit with the extra length of the wires.

Using a calculator, substitute L = [same number] into the equation above to find the extra resistance in the circuit when:

L = 2.5cm (0.025m), the resistance = 8.077 x 10-7[pic]

L = 5cm (0.05m), the resistance = 1.6154 x 10-6[pic]

L = 7.5cm (0.075m), the resistance = 2.423 x 10-6[pic]

L = 10cm (0.1m), the resistance = 3.2307 x 10-6[pic]

The above shows that the wires will have a minor effect on the circuit’s resistivity.

The effect of temperature on the resistivity of the fixed resistors in the circuit

Rt=R0{1+α(T-T0)} where for:

R1, R0 = 10k[pic] and T = 16.50C

R2, R0 = 10k[pic] and T = 170C

Where T0 = room temperature = 140C and α = copper wire = 0.004041/0C
For R1 ( Rt = 10,000 {(1 + 0.004041(16.5-14)) ( = 10,101.025[pic] (10.101K[pic])
For R2 ( Rt = 10,000 {(1 + 0.004041(17-14)) ( = 10,121.23[pic] (10.121K[pic])

For R1 (10K[pic]), there is an increase of 101.025[pic] (A total increase in resistance of 1.00%)
For R2 (10K[pic]), there is an increase of 121.23[pic] (A total increase in resistance of 1.19%)
This analysis shows that an increase in temperature of the components has an effect on the resistivity of the circuit, causing it to increase in proportion. The fixed resistors (R1 and R2) are affected by 1.00% to 1.98%.

Calculations of best pot

Using information obtained from www.bpmdatabase.com. The selected songs are shown below. Song A: 1.33 Hz

Song B: 1.86 Hz

Song C: 2.63 Hz

← [pic]

Min Min 22µF

22kΩ 10kΩ (no min)

Choice of Resistor and Pot

Calculation of Frequency Ranges

Resistor 1: R1

Port 1

Min: 22 kΩ

[pic]= 1.5461

Max: 30 kΩ

[pic]=1.2987

Port 2

Min: 35 kΩ

[pic]= 1.1806

Max: 40 kΩ

[pic]= 1.0823

Port 3

Min: 45 kΩ

[pic]= 9.9900*10-1

Max: 50 kΩ

[pic]=9.2764*10-1

Port 4

Min: 55 kΩ

[pic]= 8.6580*10-1

Max: 60 kΩ

[pic]= 8.1169*10-1

Resistor 2: R2

Port 1

Min: 100 kΩ

[pic]= 5.4113*10-1

Max: 150 kΩ

[pic]= 3.8197*10-1

Port 2

Min: 200 kΩ

[pic]= 2.9516*10-1

Max: 250 kΩ

[pic]= 2.4050*10-1

Port 3

Min: 300 kΩ

[pic]= 2.0292*10-1

Max: 350 kΩ

[pic]= 1.7550*10-1

Port 4

Min: 400 kΩ

[pic]= 1.5461*10-1

Max: 500 kΩ

[pic]= 1.2488*10-1

A frequency of 1.55 Hz is required in this experiment. This value is to be obtained using these values. The best pot that will best achieve this range is Pot 1. The potentiometer should be connected on resistor R1.