A Manual explaining the basic Components, Devices and Experimental Methods employed in an Electronic Instrumentation Lab for Scientists. MULTIMETER.

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1 A Manual explaining the basic Components, Devices and Experimental Methods employed in an Electronic Instrumentation ab for Scientists. MUTIMETER. Digital Multi Meters (or DMMs abbreviated) and Digital Volt Meters (or DVMs abbreviated) have replaced analog meters foe measuring voltages, currents and resistances. The multi meters we are using have various input jacks that accept banana plugs and one can connect the meter to the circuit under test using two banana plug leads. Depending on how we configure the meter and its leads we can measure: The voltage difference between the two leads. The current flowing through the meter from one lead to the other The resistance connected between its leads. Multi meters usually have a selector knob, which allows us to select what is to be measured and to set the full scale range of the display to handle inputs of various size. To avoid damaging the circuit before you power up the circuit under test, set the meter at its highest scale to avoid overflowing it. THE BREADBOARD. Breadboards are tools that help us build and test electric circuits. They include not only sockets for plugging in components and connecting them together, power supplies, a function generator, switches, logic displays etc. The breadboard sockets contain spring contacts. If a wire is pushed inside a socket the contacts press against it making an electrical connection. The sockets are internally connected in groups of five (horizontal rows) or groups of twenty five (vertical columns). Each power supply connects to a banana jack and also to a row of sockets running along the to edge of the unit. The three supplies +5Volts (red jack in some breadboards), +15 Volts (yellow jack in some breadboards) and 15 Volts (blue jack in some breadboards) have a common ground connection (black jack). The +15V and 15V supplies are actually adjustable using the knobs provided, from less than 5V to greater than 15V.

2 Illustration showing many of the basic features of a breadboard with internal connections shown for clarity. Note that each vertical column is broken into halves with no built in connection between the top and the bottom. The following photos show the front and the back sides of a breadboard. Observe how the sockets are shorted together at the back side of the board.

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4 MEASURING VOTAGE Voltage is always measured with respect to something usually a local ground (the breadboard ground). When connecting things is always a good idea to use color coding to help keep track of which lead is connected to what. Use a black banana lead to connect to the common input of the meter to the ground jack of the breadboard. Use a red banana plug with the V input of the meter. Since the DMM is battery powered it is said to float with respect to ground. It is therefore possible to measure the voltage drop across any circuit element by simply connecting the DMM directly across the element. Measuring Voltage. (a) An arbitrary circuit diagram is shown as an illustration on how to use a voltmeter. Note that the meter measures the voltage drop across both the resistor and the capacitor. (they have identical voltage drops since they are connected in parallel). (b) A drawing of the same circuit showing how the leads of the DMM should be connected when measuring voltage. Notice how the meter is connected in parallel with the resistor. When you operate the multi-meter always start from the scale with the highest maximum reading and then you proceed to a finer scale according to your readings. You never start measuring current from the finest scale unless you want to burn its fuse. MEASURING EECTRIC CURRENT. Current is measured by connecting a current meter (an ammeter or a DMM in its current mode) in series with the circuit element through which the current flows. Ohm s law relates the current I, voltage V and resistance R according to V = IR. (Notice that this is not a universal law of electric conduction since not ever material exhibits the property of linearity between the electric current passing through it and the voltage applied across it. Materials with such a linear relationship are being used to fabricate resistors.

5 Measuring current. (a) Schematic diagram of a series circuit consisting of a power supply a 10k potensiometer and a multimeter. (Notice that in this diagram the center tap of the potensiometer is left unconnected. If we accidentally connect it to the power supply or to the ground excessive current could flow and burn out the pot). (b) A drawing of the same circuit showing how the DMM leads should be configured to measure current. The meter is connected in series with the resistor. In order to measure current it is necessary to break the circuit in order to connect the ammeter in series to the element the current through which we want to measure. We also need to ensure ourselves that indeed the same current we want to measure passes through the ammeter as well. This is demonstrated in the following examples. Notice the way the circuit has been broken in order for the Ammeter to be inserted. EXAMPE 1: In the above circuit the Ammeter measures the current supplied by the battery. It DOES NOT measure the current through R 1, R 2 or R 3 resistors, but the sum of these three currents.

6 EXAMPE 2: In the circuit below the circuit has been broken in various parts and Ammeters have been inserted. What current is each Ammeter measuring? 1) Ammeter A1 is measuring the (total) current supplied by the 12 Volt battery. You can calculate this current by dividing the 12 Volts voltage by the net resistance seen by the battery (R 1 through R 4 in parallel). 2) Ammeter A2 is measuring the current passing through the resistance R 1. 3) Ammeter A4 is measuring the current passing through the resistance R 2. 4) Ammeter A6 is measuring the current passing through the resistance R 3. 8) Ammeter A7 is measuring the current passing through the resistance R 4. 9) Ammeter A3 is measuring the current flowing from node X to node Y. This is the sum of the currents flowing through resistances R 2, R 3 and R 4. Therefore the reading of A3 should be equal to the sum of the readings of A4 plus A6 plus A7 or the sum of the readings A4 plus A5. 10) Ammeter A5 is measuring the current flowing from node Y to node Z. This is the sum of the currents flowing through resistances R 3 and R 4. Therefore the reading of A5 should be equal to the sum of the readings of A6 plus A7.

7 EXAMPE 3: In the figure above we can see the implementation of the electronic schematic on the left with actual components and measuring devices on the right. Notice how the circuit is broken and the Ammeter inserted in series with the resistor. The current flowing through the Ammeter (and measured by it) is the same current flowing through the resistor. Caution: You need to be CAREFU when you measure EECTRIC CURRENT. There is a fuse inside the instrument to protect it from being destroyed. The fuse will burn itself if the multi-meter draws more current than the maximum allowed. Since the resistance of the multi-meter in Current measuring mode (ammeter) is very small, if the current you try to measure is larger than the maximum reading of the scale the fuse will burned and you will not be able to use it until we change it. When you operate the instrument as an ammeter always start from the scale with the highest maximum current reading and then you proceed to a finer scale according to your readings. You never start measuring current from the finest current measuring scale unless you want to burn its fuse.

8 THE EXPERIMENTS THAT YOU WI DO ARE NOT DESIGNED TO PROTECT YOUR INSTRUMENTS FROM OVEROADING. PEASE READ CAREFUY THE NEXT STATEMENTS. WHEN YOU MEASURE AN EECTRIC CURRENT BEFORE YOU TURN THE POWER ON ENSURE YOURSEVES THAT: 1. THE MUTIMETER IS SET AT THE (AC OR DC) CURRENT MEASURING MODE AND THAT IS AT THE ARGEST CURRENT SCAE. IF YOU OVEROAD THE INSTRUMENT THE FUSE WI BURN ITSEF OFF SINCE THE INTERNA RESISTANCE OF THE IDEA AMMETER IS YOU HAVE CONNECTED THE AMMETER IN SERIES WITH THE EEMENT THE CURRENT THROUGH WHICH YOU WANT TO MEASUER. IF THE CONNECTION IS ACCIDENTAY IN PARAE THE FUSE OF THE INSTRUMENT WI BURN ITSEF OFF SINCE YOU WI SHORT THE EEMENT BECAUSE OF THE OW INTERNA RESISTANCE OF THE AMMETER.

9 MEASURING RESISTANCE. Resistances usually are little cylinders of carbon, carbon film, metal film or wound up wire encased in an insulating coating with wire leads striking out the ends. Often the resistance is indicated by means of color stripes according to the resistor color code. Resistors come in various sizes according to their power rating. The common sizes are 1/8 W, ¼ W, ½ W 1 W and 2 W. The resistance in Ohms is the sum of the values in columns 1 and 2 multiplied by the value in column 3 plus or minus the tolerance in column 4. For example the color code for an 1kΩ resistor would be brown-black-red, for a 51Ω green-brown-black, for a 330Ω orange-orange-brown, etc.

10 A potentiometer is a special type of resistor that has an adjustable center-tap or slider, allowing electrical connections to be made not only at the two ends, but also at an adjustable point along the resistive material. The voltage of this adjustable point depends on the setting of the potentiometer s knob. Warning: If you accidentally connect power or ground to the potentiometer s center tap, you can easily burn it out rendering it useless. If in doubt have someone check your circuit before turning on the power. MEASURING CURRENT WITH A VOTMETER. We can use a Voltmeter to measure the current passing through a resistance. First, measure the resistance and then measure the voltage drop across the resistance with the voltmeter. Finally use Ohm s law to find out the current. This technique is very useful when the ammeter fuse is burned and we cannot measure (especially small) currents directly. We can use this technique only with resistances not with dynamic elements like diodes or transistors. CAPACITOR VAUE CODING For some type of capacitors their value (and units) appear explicitly written on their bodies. Other types of capacitors have their value encoded using color code. Certain types of small capacitors (polyester, ceramic or mylar) capacitors have their value written on them. On their body their written value is encrypted in a three digit number. The first two digits indicate the first two most significant digits of their numerical value. The third digit indicates the number of zeros after the two most significant digits. The numerical value that appears this way is in pico Farads. Example: Suppose you see the number 324 printed on the body of the capacitor. The numerical value of the Capacitance indicated is: pf or 320 nf or 0.32 µf Next to the numerical value of the capacitor a letter is usually printed indicating the tolerance of the capacitor. Here are some tolerances and the corresponding letters

11 C = ± 0.25 pf, D = ± 0.5pF, J = ± 5%, P = + 100% 0%, Y = 20% + 50%, Z K = ± 10%, M = 20% + 80% = ± 20% THE PROBE Oscilloscopes come with probes. Probes are cables that have a coaxial connector on one end for connecting to the oscilloscope and a special tip on the other for connecting to any desired point of the circuit to be tested. Top increase the scope s input impedance and affect the voltage to be measured as little as possible we can use a 10X attenuating probe which has circuitry inside that divides the signal voltage by 10. Some oscilloscopes sense the nature of the probe and automatically correct for this factor of 10; other oscilloscopes need to be told by the user which attenuation setting is in use. Note that a probe has an alligator clip that connects to the shield of the coaxial cable (ground) which is useful in reducing noise when probing high frequency or low voltage signals. Since it is connected directly to the scope s case, which is grounded via the third prong of the AC power plug, it must be never allowed to touch any point of a circuit other than the ground. Otherwise you will create a short circuit, which could damage circuit components. This is no problem if you are measuring a voltage with respect to ground. But if you want to measure a voltage drop between two points in the circuit neither of which is at ground, first observe one point then observe the other. The difference between the two measurements is the voltage drop across the element. During this process the alligator clip of the probe should always be attached firmly to ground. An attenuating probe can distort a signal. The manufacturer therefore provides a compensation adjustment screw, which needs to be tuned for minimum distortion An oscilloscope should have built in a calibration circuit that outputs a standard square wave you can use to test a probe. Display the calibration square wave signal on the scope. If the signal looks distorted carefully adjust the probe compensation using a small screwdriver.

12 THE OSCIOSCOPE Illustration of a typical digital oscilloscope. The basic features to be used are shown. Note the location of the AUTOSET button. When everything else fails try autoset. Vertical controls. There is a set of vertical controls for each oscilloscope channel. These adjust the sensitivity (Volts per vertical division on the screen) and offset (the vertical position of the beam on the screen when the input voltage is 0). The CH1 and CH2 menu buttons can be used to turn the display of each channel on and off. They also select, which control settings are programmed by the push buttons to the right of the screen. Horizontal sweep. To the right of the vertical controls there are the horizontal controls. Normally the scope displays voltage on the vertical axis and time on the horizontal. The SC/DIV knob sets the sensitivity of the horizontal axis (time per horizontal division on the screen). The POSITION knob moves the image horizontally on the screen. Triggering. Triggering is the most complicated function performed by the scope. To create a stable image of a waveform the scope must trigger its display at a particular voltage known as the trigger threshold. The display is synchronized whenever the input signal crosses that voltage, so that many images of the signal occurring one after another can be

13 superimposed on the same place on the screen. The EVE knob sets the threshold voltage for triggering. One can select whether triggering occurs when the threshold voltage is crossed from below (rising edge triggering) or from above ( falling-edge triggering) using the trigger menu (or for some scope models using trigger control knobs and switches). You can also select the signal source for the triggering circuitry to be channel 1, channel 2, an external trigger signal or the 120 V AC power line. Setting up the trigger can be tricky, that is why some oscilloscope models provide an automatic set-up feature (via the AUTOSET button) which can lock in on any repetitive signal presented at the input and adjust the voltage, the time sensitivities and the triggering for a stable display. TESTING DIODES. Diodes exhibit low resistance and allow current to flow through them when forward biased. When diodes are reverse biased they do not allow electric current to flow through then and exhibit very high (practically infinite) resistance. In order to test a diode with a multimeter we have to test it separately in the forward conducting and in the reverse blocking mode. In order to test the diode in the conducting forward mode with the multimeter we connect the positive lead of the meter to the anode and the negative lead to the cathode of the diode. For a normal Silicon diode the multimeter should display a low voltage of about 0.7 Volts, or a low resistance (between 1 and 30 Ohms). To check the diode in the blocking mode connect the positive lead of the meter to the cathode and the negative lead to the anode of the diode. The multimeter should display a very high resistance (a thousand times the low resistance or an out of range reading). Some multimeters have a special setting for diode testing. The experimental setup is shown below.

14 TESTING TRANSISTORS. Transistors can be considered as two back to back connected diodes. A PNP transistor is two pn diodes with a common N layer (N base) and an NPN transistor two pn diodes with a common P layer (P base). Both junctions should be tested separately in the forward conducting and the reverse blocking mode for each type of transistor. The way of testing is the same as described in the case of diodes. The setup for testing is shown below for a pnp transistor. In the left part of the figure the junctions are biased in the forward mode and they are registering very low resistance in the multimeter. In the right part of the figure the junctions (Collector Base and Base Emitter) are biased in the blocing mode and the multimeter is registering out of range resistance.

15 Finally the biasing the Collector Emitter leads of the transistor should always register very high resistance (non conducting mode since there is no voltage at the base). VOTAGE SOURCES. A voltage source (supply) is a device that forces a fixed voltage difference between the leads of a load independent on the resistance of the load R. The current supplied by the voltage source is calculated with the aid of Ohm s aw and the resistance of the load. A practical Voltage Source has a small output resistance r and can be approximated with an ideal voltage source in series with the small output resistance r of the non ideal supply. A good voltage power supply must have an output resistance much smaller than the load resistance in order for the voltage appearing across the load to be independent of the load itself. Also a load that accepts an input signal in voltage form must have a resistance much larger than the output resistance of the signal source (voltage source). Theoretically a voltage source must have zero output resistance and a load accepting a signal in voltage form must have infinite resistance.

16 From the figure we can calculate the current delivered by the source and flowing through the load: V I = and therefore the voltage across the load is: r out + R V R IR V rout R = = a fraction of the voltage delivered by the source. + For 100% voltage delivery the load resistance R must be much larger than the r out. Ideally R must be infinite and r out zero. CURRENT SOURCES. A current source (supply) is a device that delivers a fixed current difference at a load independent on the resistance of the load R. The voltage appearing across the load (and supplied by the current source) is calculated with the aid of Ohm s aw and the resistance of the load. A practical Current Source has a finite output resistance R out and can be approximated with an ideal current source in parallel with the output resistance R out of the non ideal supply. A good current source must have an output resistance much larger than the load resistance in order for the current through the load to be independent of the load itself and to approach the current delivered by the current source. Moreover a load that accepts an input signal in current form must have a resistance much smaller than the output resistance of the signal source (current source). Theoretically a current source must have infinite output resistance and a load accepting a signal in current form must have zero resistance.

17 From the figure we can calculate the voltage difference appearing between the leads A and B of the load: IRRout VAB = I( Rout // R ) = and therefore the current flowing through the load is: R + R out I V AB Rout I R Rout R = = a fraction of the current delivered by the source. + For 100% current delivery on the load the load resistance R must be much smaller than the R out. Ideally R must be zero and R out infinite. VOTAGE DIVIDERS. A voltage divider is two resistors in series connected to a voltage source. Portion of the voltage delivered by the source appears across each resistance and therefore two resistances in series constitute a practical way to supply to a load a smaller voltage than the voltage delivered by the source. The setup is illustrated at the figure. We can calculate the voltage difference between points A and B by employing Kirchoff rules. V = I ( R + R // R ) 1 2 I = V R + R 1 2 // R and therefore the voltage delivered to the load is: V = I where 2 ( R ) = + 2 // R V V R1 R2 // R R // 2 R R2R = R + R 2 R // R

18 We can see that the load resistance affects the operation of the voltage divider and therefore the load voltage. CURRENT DIVIDERS. A current divider is two resistors in parallel connected to a current source. One of these two resistors is the load. Only a portion of the current delivered by the source flows through each resistance and therefore two resistances in parallel constitute a practical way to supply to a load a smaller current than the one delivered by the source. The setup is illustrated at the figure. We can calculate the current flowing through the load resistance R by employing the rules of Kirchoff. The voltage across the load is: V = I // ( R R ) = V I R + R RR Therefore the current through the load is: V R I = = I I a fraction of the current delivered by the source. In practice R R + R R contains the effects of the finite output resistance of the current source appearing in parallel with any externally connected resistance to the source output. THE THEVENIN EQUIVAENT CIRCUIT. Consider an electronic device shown in the figure below. The device is shown as a black box totally opaque to the user internally containing an unknown number and type of electronic components. The complexity of the enclosed circuit is also unknown. Terminals A and B interface the device with the external world and could serve either as input or as output. The Thevenin theorem states that the circuitry between terminals A and B internal to the box can be replaced with the equivalent Thevenin circuit, a perfect voltage source supplying a voltage called the Thevenin voltage (V Th ) in series with a Resistance called the Thevenin (sometimes called also the input or output ) resistance depending on weather terminals A and B serve as device input or output). The figure shows the equivalent Thevenin circuit between terminals A and B replacing the internal components of the device.

19 Rules for finding the Thevenin Voltage: The Thevenin voltage (V Th ) is the voltage difference between the terminals A and B when they are open (and therefore no current flows into our out from the device). Here are some basic procedures to find the Thevenin Resistance: Method 1: Short Terminals A and B and measure the current flowing through shorted terminals A and B, I short. This current is also called the Norton current I N. The Thevenin Resistance is the Thevenin Voltage divided by the current through the shorted terminals A and B VTh R Th = I short Method 2: Replace all Voltage Sources with a closed switch (short) and all Current Sources with an open switch. The equivalent net resistance seen between terminals A and B is the Thevenin Resistance. Method 3: Suppose you want to measure the input (or output) Resistance of a device. Ground the output (or input if you are measuring the output resistance) and plug an ideal voltage or current source at the terminal. Calculate the current supplied by the hypothetical ideal voltage source or the voltage supplied by the hypothetical ideal current source if you

20 decide to go with a current source. Use Ohm s law to calculate the resistance seen by the source between the terminals. Method 4: Measure with a voltmeter the voltage between the terminals A and B. The voltmeter has infinite resistance (it draws no current from the device) and therefore it registers the Thevenin Voltage. Plug a load variable resistance R between the terminals A and B (use a potensiometer for this). With a voltmeter measure now the voltage drop across the load resistor. With a screwdriver vary the value of the resistor until the voltmeter registers a voltage drop across the load equal half the value of the already measured Thevenin voltage. What is the relationship between the value of that load resistance and the Thevenin Resistance between terminals A and B. Hint: The circuit is essentially a voltage divider where the Thevenin Voltage is split on the Thevenin Resistance and on the oad resistance. THE NORTON EQUIVAENT CIRCUIT. Consider the same electronic device shown in the figure below once more. The device is again shown as a black box totally opaque to the user, internally containing an unknown number and type of electronic components. The complexity of the enclosed circuit is also unknown. Terminals A and B interface the device with the external world and could serve either as input or as output.

21 The Norton theorem states that the circuitry between terminals A and B internal to the box can be replaced with the equivalent Norton circuit, an ideal Current Source supplying an electric current called the Norton (I N ) in parallel with a Resistance called the Norton (sometimes also called the input or output ) resistance depending on weather terminals A and B serve as device input or output. The Norton Resistance R N is the same as the Thevenin Resistance discussed above and therefore we already know how to find it (R N = R Th ). The figure shows the equivalent Norton circuit between terminals A and B replacing the internal components of the device. Rules for finding the Norton Current: The Norton current is the current flowing through the terminals A and B if we short them. (It is the I short current we used in the Thevenin theorem discussion to find the R Th ). USAGE OF NORTON AND THEVENIN CIRCUITS. The Thevenin and Norton equivalent circuits are being used to determine how two electrical or electronic components behave when they interact that is when they are connected in such a way so that the output of the first becomes the input of the second. Consider the situation shown in the figure below where device A (say a sensor or detector) delivers its signal to device B (say an Amplifier). Device A is considered a

22 voltage source (the output information is supposed to be the voltage) and device B is a voltage Amplifier (expects a voltage signal at its input). The output of device A (the sensor) has been replaced with its equivalent Thevenin Circuit, there the Thevenin voltage is the signal V S and the Thevenin Resistance is the output resistance of the detector say R d. The input of the amplifier has been replaced by its Thevenin rinput Resistance say R in. On the Amplifier input side there is no signal therefore there is no Thevenin Voltage or Norton Current source. We can recognize immediately the action of the voltage divider and the signal which really appears at the input of the Amplifier and being Amplified is: R V S R in in + R D which is a fraction of the useful voltage delivered by the sensor. For good matching of the two electronic devices we want this fraction to approach 100%, that is we need R in to be much larger that R D. Ideally we want the voltage source to have zero output resistance and the device accepting voltage signals to have infinite input resistance. Consider now the situation shown in the figure below where device A (say a sensor or detector) delivers its signal to device B (say an Amplifier). However now device A is considered a current source (the output information is supposed to be encoded in the form of current) and device B is a current Amplifier (expects a current signal at its input). The output of device A (the sensor) has been replaced with its equivalent Norton Circuit, there the Norton Current is the signal I S and the Norton Resistance (same as the Thevenin

23 resistance) is the output resistance of the detector say R d. The input of the amplifier has been replaced by its Thevenin (or Norton) input Resistance say R in. On the Amplifier input side there is no signal therefore there is no Thevenin Voltage or Norton Current source. We can recognize immediately the action of the current divider and the signal which really flows through R in at the input of the Amplifier and therefore being Amplified is: R I S R D in + R D which is a fraction of the useful Current Signal delivered by the sensor. For good matching of the two electronic devices we want this fraction to approach 100%, that is we need R in to be much smaller that R D. Ideally we want the current source to have infinite output resistance and the device accepting current signals to have zero input resistance (effectively shorted inputs). We see therefore that the practical usage of the Norton and Thevenin equivalent circuits in electronics is to determine how two circuits interact when they are connected and signals are propagating through them. We can model the input and/or the output of a device either with its Norton or with its Thevenin equivalent circuits. The Norton and the Thevenin resistances are the same ant the Thevenin voltage is related to the Norton current via the formula: V = I R R = R Th N Th N Th

24 The results of our analysis will be the same and independent on our choice to model it using the Thevenin or the Norton equivalent circuit. However we need to decide if we will consider the output of a device a signal or a current source based on the output resistance as well as we need to decide if the input of a device is accepting signals in voltage or in current form base on its input resistance. It is the responsibility of the experimentalist and the designer to make a good matching of the components. THE OPERATIONA AMPIFIER (Op Amp) An Operational Amplifier (otherwise called op-amp) is a Differential Amplifier incorporated in a chip as a linear integrated circuit. The Differential Amplifier is an Amplifier which amplifies the difference between two signals applied to the two inputs it has. The two inputs are indicated with the symbols: + (plus) or the non inverting input or υ + and -- (minus) or the inverting input or υ -- The output signal can be written as: υ = A ( υ υ out + ) The gain A is a very large number usually between 150,000 and 300,000. In the figure we show the schematic diagram for an op amp as it appears in electronic circuit designs. The most widespread op-amp chip is the M741 which incorporates a single amplifier per chip. The experimentalist should always study the data sheet of the M741 chip for the correct specifications and pin-out usage. In order for the chip to work it needs to be powered by a positive and a negative power supply, indicated by +Vcc and Vcc in the figure. Their values need not be the same but for most cases we select +12V and -12V (or +15V and -15V). The pin out diagram appears in the

25 Figure. Pin NC is left unconnected. For basic lab experiments the OFFSET NU pins will be left unconnected too. Note: The op-amp cannot deliver an output voltage outside the +Vcc and Vcc range. Also the op-amp cannot deliver an output current larger than a value specified at its data sheet (15 ma or 20mA for the M741 chip). The chip clips the output voltage and the output current at their limit values. The M741 has been designed to appear in linear Op-Amp Circuits with negative feedback. That is when we design electronic circuits involving the 741 op-amp a portion of its output is fed at the inverting input (negative feedback), via passive elements (usually Resistors and/or Capacitors) An example of such a circuit appears in the figure. In order to analyze such circuits we follow the following three Op-Amp rules: Rule 1: The Op-Amp has infinite input impedance and no current is flowing into it. Rule 2: The Op-Amp with a negative feedback at a linear electronic circuit works in such a way so that, both inverting (minus) and non-inverting (plus) inputs are held at the same voltage. For Example in the figure the inverting input is held at zero voltage (virtual ground) by virtue of the non inverting input that is hardwired at the ground. Rule 3: Rule number 2 does not hold if the output voltage or if the output current ar out of their limits (their specs). They cannot be out of their limits. Simply the chip clips the output voltage (or the output current) at their limiting values whatever the input voltages at the inverting and non inverting inputs may be. These rules allow us to analyze almost all linear circuits containing op amps and calculate the output voltage as a function of the input (the gain for the circuit).