Hiow to use The Summing Amplifier. step by step, simple and best guide

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The Summing Amplifier

The Summing Amplifier

The Summing Amplifier is a very flexible circuit based upon the standard Inverting Operational Amplifier configuration. As its name suggests, the “summing amplifier” can be used for combining the voltage present on multiple inputs into a single output voltage.

We saw previously in the Inverting Operational Amplifier that the inverting amplifier has a single input voltage, ( Vin ) applied to the inverting input terminal. If we add more input resistors to the input, each equal in value to the original input resistor, Rin we end up with another operational amplifier circuit called a Summing Amplifier, “summing inverter” or even a “voltage adder” circuit as shown below.

Summing Amplifier Circuit

The output voltage, ( Vout ) now becomes proportional to the sum of the input voltages, V1, V2, V3etc. Then we can modify the original equation for the inverting amplifier to take account of these new inputs thus:

However, if all the input impedances, ( Rin ) are equal in value, we can simplify the above equation to give an output voltage of:

Summing Amplifier Equation

We now have an operational amplifier circuit that will amplify each individual input voltage and produce an output voltage signal that is proportional to the algebraic “SUM” of the three individual input voltages V1, V2 and V3. We can also add more inputs if required as each individual input “see’s” their respective resistance, Rin as the only input impedance.

This is because the input signals are effectively isolated from each other by the “virtual earth” node at the inverting input of the op-amp. A direct voltage addition can also be obtained when all the resistances are of equal value and Rƒ is equal to Rin.

A Scaling Summing Amplifier can be made if the individual input resistors are “NOT” equal. Then the equation would have to be modified to:

To make the math’s a little easier, we can rearrange the above formula to make the feedback resistor RF the subject of the equation giving the output voltage as:

This allows the output voltage to be easily calculated if more input resistors are connected to the amplifiers inverting input terminal. The input impedance of each individual channel is the value of their respective input resistors, ie, R1, R2, R3 … etc.

Sometimes we need a summing circuit to just add together two or more voltage signals without any amplification. By putting all of the resistances of the circuit above to the same value R, the op-amp will have a voltage gain of unity and an output voltage equal to the direct sum of all the input voltages as shown:

The Summing Amplifier is a very flexible circuit indeed, enabling us to effectively “Add” or “Sum” (hence its name) together several individual input signals. If the inputs resistors, R1, R2, R3 etc, are all equal a “unity gain inverting adder” will be made. However, if the input resistors are of different values a “scaling summing amplifier” is produced which will output a weighted sum of the input signals.

Summing Amplifier Example No1

Find the output voltage of the following Summing Amplifier circuit.

Summing Amplifier

Using the previously found formula for the gain of the circuit

We can now substitute the values of the resistors in the circuit as follows,

We know that the output voltage is the sum of the two amplified input signals and is calculated as:

Then the output voltage of the Summing Amplifier circuit above is given as -45 mV and is negative as its an inverting amplifier.

Summing Amplifier Applications

So what can we use summing amplifiers for?. If the input resistances of a summing amplifier are connected to potentiometers the individual input signals can be mixed together by varying amounts. For example, measuring temperature, you could add a negative offset voltage to make the output voltage or display read “0” at the freezing point or produce an audio mixer for adding or mixing together individual waveforms (sounds) from different source channels (vocals, instruments, etc) before sending them combined to an audio amplifier.

Summing Amplifier Audio Mixer

Another useful application of a Summing Amplifier is as a weighted sum digital-to-analogue converter. If the input resistors, Rin of the summing amplifier double in value for each input, for example, 1kΩ, 2kΩ, 4kΩ, 8kΩ, 16kΩ, etc, then a digital logical voltage, either a logic level “0” or a logic level “1” on these inputs will produce an output which is the weighted sum of the digital inputs. Consider the circuit below.

Digital to Analogue Converter

Of course this is a simple example. In this DAC summing amplifier circuit, the number of individual bits that make up the input data word, and in this example 4-bits, will ultimately determine the output step voltage as a percentage of the full-scale analogue output voltage.

Also, the accuracy of this full-scale analogue output depends on voltage levels of the input bits being consistently 0V for “0” and consistently 5V for “1” as well as the accuracy of the resistance values used for the input resistors, Rin.

Fortunately to overcome these errors, at least on our part, commercially available Digital-to Analogue and Analogue-to Digital devices are readily available with highly accurate resistor ladder networks already built-in.

In the next tutorial about Operational Amplifiers, we will examine the effect of the output voltage,Vout when a signal voltage is connected to the inverting input and the non-inverting input at the same time to produce another common type of operational amplifier circuit called a Differential Amplifier which can be used to “subtract” the voltages present on its inputs.

What is Non-inverting Operational Amplifier Electronics Learning. step by step, simple and best article to learn today

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Non-inverting Operational Amplifier

The Non-inverting Operational Amplifier

The second basic configuration of an operational amplifier circuit is that of a Non-inverting Operational Amplifier. In this configuration, the input voltage signal, ( Vin ) is applied directly to the non-inverting ( + ) input terminal which means that the output gain of the amplifier becomes “Positive” in value in contrast to the “Inverting Amplifier” circuit we saw in the last tutorial whose output gain is negative in value. The result of this is that the output signal is “in-phase” with the input signal.

Feedback control of the Non-inverting Operational Amplifier is achieved by applying a small part of the output voltage signal back to the inverting ( – ) input terminal via a Rƒ – R2 voltage divider network, again producing negative feedback. This closed-loop configuration produces a non-inverting amplifier circuit with very good stability, a very high input impedance, Rin approaching infinity, as no current flows into the positive input terminal, (ideal conditions) and a low output impedance, Rout as shown below.

Non-inverting Operational Amplifier Configuration

In the previous Inverting Amplifier tutorial, we said that for an ideal op-amp “No current flows into the input terminal” of the amplifier and that “V1 always equals V2”. This was because the junction of the input and feedback signal ( V1 ) are at the same potential.

In other words the junction is a “virtual earth” summing point. Because of this virtual earth node the resistors, Rƒ and R2 form a simple potential divider network across the non-inverting amplifier with the voltage gain of the circuit being determined by the ratios of R2 and Rƒ as shown below.

Equivalent Potential Divider Network

Then using the formula to calculate the output voltage of a potential divider network, we can calculate the closed-loop voltage gain ( A V ) of the Non-inverting Amplifier as follows:

Then the closed loop voltage gain of a Non-inverting Operational Amplifier will be given as:

We can see from the equation above, that the overall closed-loop gain of a non-inverting amplifier will always be greater but never less than one (unity), it is positive in nature and is determined by the ratio of the values of Rƒ and R2.

If the value of the feedback resistor Rƒ is zero, the gain of the amplifier will be exactly equal to one (unity). If resistor R2 is zero the gain will approach infinity, but in practice it will be limited to the operational amplifiers open-loop differential gain, ( Ao ).

We can easily convert an inverting operational amplifier configuration into a non-inverting amplifier configuration by simply changing the input connections as shown.

Voltage Follower (Unity Gain Buffer)

If we made the feedback resistor, Rƒ equal to zero, (Rƒ = 0), and resistor R2 equal to infinity, (R2 = ∞), then the circuit would have a fixed gain of “1” as all the output voltage would be present on the inverting input terminal (negative feedback). This would then produce a special type of the non-inverting amplifier circuit called a Voltage Follower or also called a “unity gain buffer”.

As the input signal is connected directly to the non-inverting input of the amplifier the output signal is not inverted resulting in the output voltage being equal to the input voltage, Vout = Vin. This then makes the voltage follower circuit ideal as a Unity Gain Buffer circuit because of its isolation properties.

The advantage of the unity gain voltage follower is that it can be used when impedance matching or circuit isolation is more important than amplification as it maintains the signal voltage. The input impedance of the voltage follower circuit is very high, typically above 1MΩ as it is equal to that of the operational amplifiers input resistance times its gain ( Rin x Ao ). Also its output impedance is very low since an ideal op-amp condition is assumed.

Non-inverting Voltage Follower

In this non-inverting circuit configuration, the input impedance Rin has increased to infinity and the feedback impedance Rƒ reduced to zero. The output is connected directly back to the negative inverting input so the feedback is 100% and Vin is exactly equal to Vout giving it a fixed gain of 1 or unity. As the input voltage Vin is applied to the non-inverting input the gain of the amplifier is given as:

Since no current flows into the non-inverting input terminal the input impedance is infinite (ideal op-amp) and also no current flows through the feedback loop so any value of resistance may be placed in the feedback loop without affecting the characteristics of the circuit as no voltage is dissipated across it, zero current flows, zero voltage drop, zero power loss.

Since the input current is zero giving zero input power, the voltage follower can provide a large power gain. However in most real unity gain buffer circuits a low value (typically 1kΩ) resistor is required to reduce any offset input leakage currents, and also if the operational amplifier is of a current feedback type.

The voltage follower or unity gain buffer is a special and very useful type of Non-inverting amplifier circuit that is commonly used in electronics to isolated circuits from each other especially in High-order state variable or Sallen-Key type active filters to separate one filter stage from the other. Typical digital buffer IC’s available are the 74LS125 Quad 3-state buffer or the more common 74LS244 Octal buffer.

One final thought, the closed loop voltage gain of a voltage follower circuit is “1” or Unity. The open loop voltage gain of an operational amplifier with no feedback is Infinite. Then by carefully selecting the feedback components we can control the amount of gain produced by a non-inverting operational amplifier anywhere from one to infinity.

Thus far we have analysed an inverting and non-inverting amplifier circuit that has just one input signal, Vin. In the next tutorial about Operational Amplifiers, we will examine the effect of the output voltage, Vout by connecting more inputs to the amplifier. This then produces another common type of operational amplifier circuit called a Summing Amplifier which can be used to “add” together the voltages present on its inputs.

How to use operation amplifiers in electronic circuits. step by step, easy and top guide to learn quickly

Operational Amplifier Basics

Operational Amplifier Basics

As well as resistors and capacitors, Operational Amplifiers, or Op-amps as they are more commonly called, are one of the basic building blocks of Analogue Electronic Circuits.Operational amplifiers are linear devices that have all the properties required for nearly ideal DC amplification and are therefore used extensively in signal conditioning, filtering or to perform mathematical operations such as add, subtract, integration and differentiation.

An Operational Amplifier, or op-amp for short, is fundamentally a voltage amplifying device designed to be used with external feedback components such as resistors and capacitors between its output and input terminals. These feedback components determine the resulting function or “operation” of the amplifier and by virtue of the different feedback configurations whether resistive, capacitive or both, the amplifier can perform a variety of different operations, giving rise to its name of “Operational Amplifier”.

An Operational Amplifier is basically a three-terminal device which consists of two high impedance inputs, one called the Inverting Input, marked with a negative or “minus” sign, ( - ) and the other one called the Non-inverting Input, marked with a positive or “plus” sign ( + ).

The third terminal represents the Operational Amplifiers output port which can both sink and source either a voltage or a current. In a linear operational amplifier, the output signal is the amplification factor, known as the amplifiers gain ( A ) multiplied by the value of the input signal and depending on the nature of these input and output signals, there can be four different classifications of operational amplifier gain.

• Voltage  – Voltage “in” and Voltage “out”
• Current  – Current “in” and Current “out”
• Transconductance  – Voltage “in” and Current “out”
• Transresistance  – Current “in” and Voltage “out”

Since most of the circuits dealing with operational amplifiers are voltage amplifiers, we will limit the tutorials in this section to voltage amplifiers only, (Vin and Vout).

The output voltage signal from an Operational Amplifier is the difference between the signals being applied to its two individual inputs. In other words, an op-amps output signal is the difference between the two input signals as the input stage of an Operational Amplifier is in fact a differential amplifier as shown below.

Differential Amplifier

The circuit below shows a generalized form of a differential amplifier with two inputs marked V1and V2. The two identical transistors TR1 and TR2 are both biased at the same operating point with their emitters connected together and returned to the common rail, -Vee by way of resistor Re.

Differential Amplifier

The circuit operates from a dual supply +Vccand -Vee which ensures a constant supply. The voltage that appears at the output, Vout of the amplifier is the difference between the two input signals as the two base inputs are in anti-phase with each other.

So as the forward bias of transistor, TR1 is increased, the forward bias of transistor TR2 is reduced and vice versa. Then if the two transistors are perfectly matched, the current flowing through the common emitter resistor,Re will remain constant.

Like the input signal, the output signal is also balanced and since the collector voltages either swing in opposite directions (anti-phase) or in the same direction (in-phase) the output voltage signal, taken from between the two collectors is, assuming a perfectly balanced circuit the zero difference between the two collector voltages.

This is known as the Common Mode of Operation with the common mode gain of the amplifier being the output gain when the input is zero.

Operational Amplifiers also have one output (although there are ones with an additional differential output) of low impedance that is referenced to a common ground terminal and it should ignore any common mode signals that is, if an identical signal is applied to both the inverting and non-inverting inputs there should no change to the output.

However, in real amplifiers there is always some variation and the ratio of the change to the output voltage with regards to the change in the common mode input voltage is called the Common Mode Rejection Ratio or CMRR.

Operational Amplifiers on their own have a very high open loop DC gain and by applying some form of Negative Feedback we can produce an operational amplifier circuit that has a very precise gain characteristic that is dependant only on the feedback used. Note that the term “open loop” means that there are no feedback components used around the amplifier so the feedback path or loop is open.

An operational amplifier only responds to the difference between the voltages on its two input terminals, known commonly as the “Differential Input Voltage” and not to their common potential. Then if the same voltage potential is applied to both terminals the resultant output will be zero. An Operational Amplifiers gain is commonly known as the Open Loop Differential Gain, and is given the symbol (Ao).

Equivalent Circuit of an Ideal Operational Amplifier

Op-amp Parameter and Idealised Characteristic

• Open Loop Gain, (Avo)

  • Infinite – The main function of an operational amplifier is to amplify the input signal and the more open loop gain it has the better. Open-loop gain is the gain of the op-amp without positive or negative feedback and for such an amplifier the gain will be infinite but typical real values range from about 20,000 to 200,000.

• Input impedance, (Zin)

  • Infinite – Input impedance is the ratio of input voltage to input current and is assumed to be infinite to prevent any current flowing from the source supply into the amplifiers input circuitry ( Iin = 0 ). Real op-amps have input leakage currents from a few pico-amps to a few milli-amps.

• Output impedance, (Zout)

  • Zero – The output impedance of the ideal operational amplifier is assumed to be zero acting as a perfect internal voltage source with no internal resistance so that it can supply as much current as necessary to the load. This internal resistance is effectively in series with the load thereby reducing the output voltage available to the load. Real op-amps have output impedances in the 100-20kΩ range.

• Bandwidth, (BW)

  • Infinite – An ideal operational amplifier has an infinite frequency response and can amplify any frequency signal from DC to the highest AC frequencies so it is therefore assumed to have an infinite bandwidth. With real op-amps, the bandwidth is limited by the Gain-Bandwidth product (GB), which is equal to the frequency where the amplifiers gain becomes unity.

• Offset Voltage, (Vio)

  • Zero – The amplifiers output will be zero when the voltage difference between the inverting and the non-inverting inputs is zero, the same or when both inputs are grounded. Real op-amps have some amount of output offset voltage.

From these “idealized” characteristics above, we can see that the input resistance is infinite, so no current flows into either input terminal (the “current rule”) and that the differential input offset voltage is zero (the “voltage rule”). It is important to remember these two properties as they will help us understand the workings of the Operational Amplifier with regards to the analysis and design of op-amp circuits.

However, real Operational Amplifiers such as the commonly available uA741, for example do not have infinite gain or bandwidth but have a typical “Open Loop Gain” which is defined as the amplifiers output amplification without any external feedback signals connected to it and for a typical operational amplifier is about 100dB at DC (zero Hz). This output gain decreases linearly with frequency down to “Unity Gain” or 1, at about 1MHz and this is shown in the following open loop gain response curve.

Open-loop Frequency Response Curve

From this frequency response curve we can see that the product of the gain against frequency is constant at any point along the curve. Also that the unity gain (0dB) frequency also determines the gain of the amplifier at any point along the curve. This constant is generally known as the Gain Bandwidth Product or GBP. Therefore:

GBP = Gain x Bandwidth or A x BW.

For example, from the graph above the gain of the amplifier at 100kHz is given as 20dB or 10, then the gain bandwidth product is calculated as:

GBP = A x BW = 10 x 100,000Hz = 1,000,000.

Similarly, the operational amplifiers gain at 1kHz = 60dB or 1000, therefore the GBP is given as:

GBP = A x BW = 1,000 x 1,000Hz = 1,000,000. The same!.

The Voltage Gain (AV) of the operational amplifier can be found using the following formula:

and in Decibels or (dB) is given as:

An Operational Amplifiers Bandwidth

The operational amplifiers bandwidth is the frequency range over which the voltage gain of the amplifier is above 70.7% or -3dB (where 0dB is the maximum) of its maximum output value as shown below.

Here we have used the 40dB line as an example. The -3dB or 70.7% of Vmax down point from the frequency response curve is given as 37dB. Taking a line across until it intersects with the main GBP curve gives us a frequency point just above the 10kHz line at about 12 to 15kHz. We can now calculate this more accurately as we already know the GBP of the amplifier, in this particular case 1MHz.

Operational Amplifier Example No1.

Using the formula 20 log (A), we can calculate the bandwidth of the amplifier as:

37 = 20 log A   therefore, A = anti-log (37 ÷ 20) = 70.8

GBP ÷ A = Bandwidth,  therefore, 1,000,000 ÷ 70.8 = 14,124Hz, or 14kHz

Then the bandwidth of the amplifier at a gain of 40dB is given as 14kHz as previously predicted from the graph.

Operational Amplifier Example No2.

If the gain of the operational amplifier was reduced by half to say 20dB in the above frequency response curve, the -3dB point would now be at 17dB. This would then give the operational amplifier an overall gain of 7.08, therefore A = 7.08.

If we use the same formula as above, this new gain would give us a bandwidth of approximately141.2kHz, ten times more than the frequency given at the 40dB point. It can therefore be seen that by reducing the overall “open loop gain” of an operational amplifier its bandwidth is increased and visa versa.

In other words, an operational amplifiers bandwidth is inversely proportional to its gain, ( A 1/∝ BW ). Also, this -3dB corner frequency point is generally known as the “half power point”, as the output power of the amplifier is at half its maximum value as shown:

Operational Amplifiers Summary

We know now that an Operational amplifiers is a very high gain DC differential amplifier that uses one or more external feedback networks to control its response and characteristics. We can connect external resistors or capacitors to the op-amp in a number of different ways to form basic “building Block” circuits such as, Inverting, Non-Inverting, Voltage Follower, Summing, Differential, Integrator and Differentiator type amplifiers.

Op-amp Symbol

An “ideal” or perfect Operational Amplifier is a device with certain special characteristics such as infinite open-loop gain Ao, infinite input resistance Rin, zero output resistance Rout, infinite bandwidth 0 to ∞and zero offset (the output is exactly zero when the input is zero).

There are a very large number of operational amplifier IC’s available to suit every possible application from standard bipolar, precision, high-speed, low-noise, high-voltage, etc, in either standard configuration or with internal Junction FET transistors.

Operational amplifiers are available in IC packages of either single, dual or quad op-amps within one single device. The most commonly available and used of all operational amplifiers in basic electronic kits and projects is the industry standard μA-741.

In the next tutorial about Operational Amplifiers, we will use negative feedback connected around the op-amp to produce a standard closed-loop amplifier circuit called an Inverting Amplifiercircuit that produces an output signal which is 180o “out-of-phase” with the input.