Showing posts with label Sensors. Show all posts
Showing posts with label Sensors. Show all posts

Non-inverting Amplifier

The Non-inverting Amplifier

The second basic configuration of an operational amplifier circuit is that of a Non-inverting 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 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 Amplifier Configuration

Non-inverting Amplifier

In the previous Inverting Amplifier tutorial, we said that "no current flows into the input" of the amplifier and that "V1 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,  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  as shown below.

Equivalent Potential Divider Network

Non-inverting Amplifier Potential Divider
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:
Non-inverting Amplifier Gain Calculation
Then the closed loop voltage gain of a Non-inverting Amplifier is given as:
Non-inverting Amplifier Gain

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  and R2. If the value of the feedback resistor  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.
Non-inverting Amplifier Configuration

Voltage Follower (Unity Gain Buffer)

If we made the feedback resistor,  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 thevoltage follower circuit ideal as a Unity Gain Buffer circuit because of its isolation properties as impedance or circuit isolation is more important than amplification while maintaining 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.

Voltage Follower

Voltage Follower Circuit
In this non-inverting circuit configuration, the input impedance Rin has increased to infinity and the feedback impedance  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:
Unity Gain Buffer
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 amplifiercircuit 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 output voltage gain of the voltage follower circuit with closed loop gain is Unity, the voltage gain of an ideal operational amplifier with open loop gain (no feedback) is Infinite. Then by carefully selecting the feedback components we can control the amount of gain produced by an 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.

Inverting Amplifier

The Inverting Amplifier

We saw in the last tutorial that the Open Loop Gain, ( Avo ) of an ideal operational amplifier can be very high, as much as 1,000,000 (120dB) or more. However, this very high gain is of no real use to us as it
makes the amplifier both unstable and hard to control as the smallest of input signals, just a few micro-volts, (μV) would be enough to cause the output voltage to saturate and swing towards one or the other of the voltage supply rails losing complete control of the output.
As the open loop DC gain of an operational amplifier is extremely high we can therefore afford to lose some of this high gain by connecting a suitable resistor across the amplifier from the output terminal back to the inverting input terminal to both reduce and control the overall gain of the amplifier. This then produces and effect known commonly as Negative Feedback, and thus produces a very stable Operational Amplifier based system.
Negative Feedback is the process of "feeding back" a fraction of the output signal back to the input, but to make the feedback negative, we must feed it back to the negative or "inverting input" terminal of the op-amp using an external Feedback Resistor called . This feedback connection between the output and the inverting input terminal forces the differential input voltage towards zero.
This effect produces a closed loop circuit to the amplifier resulting in the gain of the amplifier now being called its Closed-loop Gain. Then a closed-loop inverting amplifier uses negative feedback to accurately control the overall gain of the amplifier, but at a cost in the reduction of the amplifiers bandwidth.
This negative feedback results in the inverting input terminal having a different signal on it than the actual input voltage as it will be the sum of the input voltage plus the negative feedback voltage giving it the label or term of a Summing Point. We must therefore separate the real input signal from the inverting input by using an Input ResistorRin.
As we are not using the positive non-inverting input this is connected to a common ground or zero voltage terminal as shown below, but the effect of this closed loop feedback circuit results in the voltage potential at the inverting input being equal to that at the non-inverting input producing a Virtual Earthsumming point because it will be at the same potential as the grounded reference input. In other words, the op-amp becomes a "differential amplifier".

Inverting Amplifier Configuration

Inverting Amplifier

In this Inverting Amplifier circuit the operational amplifier is connected with feedback to produce a closed loop operation. For ideal op-amps there are two very important rules to remember about inverting amplifiers, these are: "no current flows into the input terminal" and that "V1 equals V2", (in real world op-amps both of these rules are broken).
This is because the junction of the input and feedback signal ( X ) is at the same potential as the positive ( + ) input which is at zero volts or ground then, the junction is a "Virtual Earth". Because of this virtual earth node the input resistance of the amplifier is equal to the value of the input resistor, Rin and the closed loop gain of the inverting amplifier can be set by the ratio of the two external resistors.
We said above that there are two very important rules to remember about Inverting Amplifiers or any operational amplifier for that matter and these are.
  • 1.  No Current Flows into the Input Terminals
  • 2.  The Differential Input Voltage is Zero as V1 = V2 = 0 (Virtual Earth)
Then by using these two rules we can derive the equation for calculating the closed-loop gain of an inverting amplifier, using first principles.
Current ( i ) flows through the resistor network as shown.
Resistor Feedback Network

Gain Calculation
Then, the Closed-Loop Voltage Gain of an Inverting Amplifier is given as.
Inverting Amplifier Gain
and this can be transposed to give Vout as:
Inverting Operational Amplifier Gain Formula
Linear Output
Linear Output
The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180o out of phase. This is due to the feedback being negative in value.
The equation for the output voltage Vout also shows that the circuit is linear in nature for a fixed amplifier gain as Vout = Vin x Gain. This property can be very useful for converting a smaller sensor signal to a much larger voltage.
Another useful application of an inverting amplifier is that of a "transresistance amplifier" circuit. ATransresistance Amplifier also known as a "transimpedance amplifier", is basically a current-to-voltage converter (Current "in" and Voltage "out"). They can be used in low-power applications to convert a very small current generated by a photo-diode or photo-detecting device etc, into a usable output voltage which is proportional to the input current as shown.

Transresistance Amplifier Circuit

Transresistance Amplifier Circuit

The simple light-activated circuit above, converts a current generated by the photo-diode into a voltage. The feedback resistor  sets the operating voltage point at the inverting input and controls the amount of output. The output voltage is given as Vout = Is x Rƒ. Therefore, the output voltage is proportional to the amount of input current generated by the photo-diode.

Example No1

Find the closed loop gain of the following inverting amplifier circuit.
Inverting Op-amp Circuit
Using the previously found formula for the gain of the circuit
Op-amp Gain
we can now substitute the values of the resistors in the circuit as follows,
Rin = 10kΩ  and  Rƒ = 100kΩ.
and the gain of the circuit is calculated as    -Rƒ/Rin = 100k/10k = 10.
therefore, the closed loop gain of the inverting amplifier circuit above is given 10 or 20dB (20log(10)).

Example No2

The gain of the original circuit is to be increased to 40 (32dB), find the new values of the resistors required.
Assume that the input resistor is to remain at the same value of 10KΩ, then by re-arranging the closed loop voltage gain formula we can find the new value required for the feedback resistor .
   Gain = -Rƒ/Rin
therefore,   Rƒ = Gain x Rin
  Rƒ = 40 x 10,000
  Rƒ = 400,000 or 400KΩ
The new values of resistors required for the circuit to have a gain of 40 would be,
 Rin = 10KΩ  and  Rƒ = 400KΩ.
The formula could also be rearranged to give a new value of Rin, keeping the same value of .
One final point to note about the Inverting Amplifier configuration for an operational amplifier, if the two resistors are of equal value, Rin = Rƒ  then the gain of the amplifier will be -1 producing a complementary form of the input voltage at its output as Vout = -Vin. This type of inverting amplifier configuration is generally called a Unity Gain Inverter of simply an Inverting Buffer.

Operational Amplifiers

Ideal Operational Amplifiers

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 ideal 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 op-amps 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 amplified output signal of an Operational Amplifier is the difference between the two signals being applied to the two inputs. In other words the output signal is a differential signal between the two inputs and 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 V1 and 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 Input
Differential Amplifier
The circuit operates from a dual supply+Vcc and -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.
Ideal 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 ofNegative Feedback we can produce an operational amplifier circuit that has a very precise gain characteristic that is dependant only on the feedback used. 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 theOpen Loop Differential Gain, and is given the symbol (Ao).

Equivalent Circuit for Ideal Operational Amplifiers

ideal operational amplifier

Op-amp Idealized Characteristics

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 an ideal 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-impedance in the 100-20Ω 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

Open-loop Frequency Response
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 = 20dB or 10, then the
GBP = 100,000Hz x 10 = 1,000,000.
Similarly, a gain at 1kHz = 60dB or 1000, therefore the
GBP = 1,000 x 1,000 = 1,000,000The same!.
The Voltage Gain (A) of the amplifier can be found using the following formula:
voltage gain
and in Decibels or (dB) is given as:
dB gain

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.
Frequency Response Curve
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.

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.

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 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 proportional to its gain. Also, this -3dB point is generally known as the "half power point", as the output power of the amplifier is at half its maximum value at this value.

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.
Operational Amplifier Symbol
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 JFET 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.
uA741 Operational Amplifier

Sound Transducer

The Sound Transducer

Sound TransducerSound is the general name given to "acoustic waves" that have frequencies ranging from just 1Hz up to many tens of thousands of Hertz with the upper
limit of human hearing being around the 20 kHz, (20,000Hz) range. The sound we hear is basically made up from mechanical vibrations produced by aSound Transducer to generate the acoustic waves and for sound to be "heard" it requires a medium for transmission either through the air, a liquid, or a solid.

Piezo Sound Transducer
Also, sound need not be a continuous frequency sound wave such as a single tone or a musical note, but may be an acoustic wave made from a mechanical vibration, noise or even a single pulse of sound such as a "bang".
Sound Transducers include both sensors, that convert sound into and electrical signal such as a microphone, and actuators that convert the electrical signals back into sound such as a loudspeaker. We tend to think of sound as only existing in the range of frequencies detectable by the human ear, from 20Hz up to 20kHz (a typical loudspeaker frequency response).
But sound transducers can also both detect and transmit sound from very low frequencies called infra-sound up to very high frequencies called ultrasound. But in order for a sound transducer to either detect or produce "sound" we first need to understand what sound is?.
Sound is basically a waveform that is produced by some form of a mechanical vibration such as a tuning fork, and which has a "frequency" determined by the origin of the sound for example, a bass drum has a low frequency sound while a cymbal has a higher frequency sound.
A sound waveform has the same characteristics as that of an electrical waveform which areWavelength (λ), Frequency (ƒ) and Velocity (m/s). Both the sounds frequency and wave shape are determined by the origin or vibration that originally produced the sound but the velocity is dependent upon the medium of transmission (air, water etc.) that carries the sound wave. The relationship between wavelength, velocity and frequency is given below as:

Sound Wave Relationship

A Sound Wave
Relationship between frequency, wavelength
  • Where:
  •   Wavelength is the time period of one complete cycle in Seconds.
  •   Frequency is the number of wavelengths per second in Hertz. 
  •   Velocity is the speed of sound through a transmission medium in m/s-1.

The Microphone Transducer

The Microphone, also called a "mic", is a sound transducer that can be classed as a "sound sensor". This is because it produces an electrical analogue output signal which is proportional to the "acoustic" sound wave acting upon its flexible diaphragm. This signal is an "electrical image" representing the characteristics of the acoustic waveform. Generally, the output signal from a microphone is an analogue signal either in the form of a voltage or current which is proportional to the actual sound wave.
The most common types of microphones available as sound transducers are DynamicElectret CondenserRibbon and the newer Piezo-electric Crystal types. Typical applications for microphones as a sound transducer include audio recording, reproduction, broadcasting as well as telephones, television, digital computer recording and body scanners, where ultrasound is used in medical applications. An example of a simple "Dynamic" microphone is shown below.

Dynamic Moving-coil Microphone Sound Transducer

Dynamic Moving Coil Microphone Sound Transducer

The construction of a dynamic microphone resembles that of a loudspeaker, but in reverse. It is a moving coil type microphone which uses electromagnetic induction to convert the sound waves into an electrical signal. It has a very small coil of thin wire suspended within the magnetic field of a permanent magnet. As the sound wave hits the flexible diaphragm, the diaphragm moves back and forth in response to the sound pressure acting upon it causing the attached coil of wire to move within the magnetic field of the magnet.
The movement of the coil within the magnetic field causes a voltage to be induced in the coil as defined by Faraday's Law of Electromagnetic Induction. The resultant output voltage signal from the coil is proportional to the pressure of the sound wave acting upon the diaphragm so the louder or stronger the sound wave the larger the output signal will be, making this type of microphone design pressure sensitive.
As the coil of wire is usually very small the range of movement of the coil and attached diaphragm is also very small producing a very linear output signal which is 90o out of phase to the sound signal. Also, because the coil is a low impedance inductor, the output voltage signal is also very low so some form of "pre-amplification" of the signal is required.
As the construction of this type of microphone resembles that of a loudspeaker, it is also possible to use an actual loudspeaker as a microphone. Obviously, the average quality of a loudspeaker will not be as good as that for a studio type recording microphone but the frequency response of a reasonable speaker is actually better than that of a cheap "freebie" microphone. Also the coils impedance of a typical loudspeaker is different at between 8 to 16Ω. Common applications where speakers are generally used as microphones are in intercoms and walki-talkie's.

The Loudspeaker Transducer

Sound can also be used as an output device to produce an alert noise or act as an alarm, and loudspeakers, buzzers, horns and sounders are all types of sound transducer that can be used for this purpose with the most commonly used audible type actuator being the "Loudspeaker".
Loudspeaker Sound Transducer
Loudspeaker Transducer
Loudspeakers are also sound transducers that are classed as "sound actuators" and are the exact opposite of microphones. Their job is to convert complex electrical analogue signals into sound waves being as close to the original input signal as possible.
Loudspeakers are available in all shapes, sizes and frequency ranges with the more common types being moving coil, electrostatic, isodynamic and piezo-electric. Moving coil type loudspeakers are by far the most commonly used speaker in electronic circuits and kits, and it is this type of sound transducer we will examine below.
The principle of operation of the Moving Coil Loudspeaker is the exact opposite to that of the "Dynamic Microphone" we look at above. A coil of fine wire, called the "speech or voice coil", is suspended within a very strong magnetic field, and is attached to a paper or Mylar cone, called a "diaphragm" which itself is suspended at its edges to a metal frame or chassis. Then unlike the microphone which is pressure sensitive, this type of sound transducer is a pressure generating device.

Moving Coil Loudspeaker

Moving Coil Loudspeaker

When an analogue signal passes through the voice coil of the speaker, an electro-magnetic field is produced and whose strength is determined by the current flowing through the "voice" coil, which inturn is determined by the volume control setting of the driving amplifier. The electro-magnetic force produced by this field opposes the main permanent magnetic field around it and tries to push the coil in one direction or the other depending upon the interaction between the north and south poles.
As the voice coil is permanently attached to the cone/diaphragm this also moves in tandem and its movement causes a disturbance in the air around it thus producing a sound or note. If the input signal is a continuous sine wave then the cone will move in and out acting like a piston pushing and pulling the air as it moves and a continuous single tone will be heard representing the frequency of the signal. The strength and therefore its velocity, by which the cone moves and pushes the surrounding air produces the loudness of the sound.
As the speech or voice coil is essentially a coil of wire it has, like an inductor an impedance value. This value for most loudspeakers is between 4 and 16Ω's and is called the "nominal impedance" value of the speaker measured at 0Hz, or DC It is important to always match the output impedance of the amplifier with the nominal impedance of the speaker to obtain maximum power transfer between the amplifier and speaker with most amplifier-speaker combinations having and efficiency rating as low as 1 or 2%.
Although disputed by some, the selection of good speaker cable is also an important factor in the efficiency of the speaker, as the internal capacitance and magnetic flux characteristics of the cable change with the signal frequency, thereby causing both frequency and phase distortion attenuating the input signal. Also, with high power amplifiers large currents are flowing through these cables so small thin bell wire type cables can overheat during extended periods of use.
The human ear can generally hear sounds from between 20Hz to 20kHz, and the frequency response of modern loudspeakers called general purpose speakers are tailored to operate within this frequency range as well as headphones, earphones and other types of commercially available headsets used as sound transducers. However, for high performance High Fidelity (Hi-Fi) type audio systems, the frequency response of the sound is split up into different smaller sub-frequencies thereby improving both the loudspeakers efficiency and overall sound quality as follows:

Generalised Frequency Ranges

Descriptive UnitFrequency Range
Sub-Woofer10Hz to 100Hz
Bass20Hz to 3kHz
Mid-Range1kHz to 10kHz
Tweeter3kHz to 30kHz

In multi speaker enclosures which have a separate Woofer, Tweeter and Mid-range speakers housed together within a single enclosure, a passive or active "crossover" network is used to ensure that the audio signal is accurately split and reproduced by all the different sub-speakers. This crossover network consists of ResistorsInductorsCapacitorsRLC type passive filters or op-amp active filters whose crossover or cut-off frequency point is finely tuned to that of the individual loudspeakers characteristics and an example of a multi-speaker "Hi-fi" type design is given below.

Multi-speaker (Hi-Fi) Design

Multispeaker Sound Transducer

 we have looked at different Sound Transducers that can be used to both detect and generate sound waves. Microphones and loudspeakers are the most commonly available sound transducer, but other lots of other types of sound transducers available which use piezoelectric devices to detect very high frequencies, hydrophones designed to be used underwater for detecting underwater sounds and sonar transducers which both transmit and recieve sound waves to detect submarines and ships.

DC Motor

Electrical Motors

Small DC MotorElectrical Motors are continuous actuators that convert electrical energy into mechanical energy in the form of a continuous angular
rotation that can be used to rotate pumps, fans, compressors, wheels, etc. As well as rotary motors, linear motors are also available. There are basically three types of conventional electrical motor available: AC type Motors, DC type Motors and Stepper Motors.

A Typical Small DC Motor
AC Motors are generally used in high power single or multi-phase industrial applications were a constant rotational torque and speed is required to control large loads. In this tutorial on motors we will look only at simple light duty DC Motors and Stepper Motors which are used in many electronics, positional control, microprocessor, PIC and robotic circuits.

The DC Motor

The DC Motor or Direct Current Motor to give it its full title, is the most commonly used actuator for producing continuous movement and whose speed of rotation can easily be controlled, making them ideal for use in applications were speed control, servo type control, and/or positioning is required. A DC motor consists of two parts, a "Stator" which is the stationary part and a "Rotor" which is the rotating part. The result is that there are basically three types of DC Motor available.
  • Brushed Motor - This type of motor produces a magnetic field in a wound rotor (the part that rotates) by passing an electrical current through a commutator and carbon brush assembly, hence the term "Brushed". The stators (the stationary part) magnetic field is produced by using either a wound stator field winding or by permanent magnets. Generally brushed DC motors are cheap, small and easily controlled.
  • Brushless Motor - This type of motor produce a magnetic field in the rotor by using permanent magnets attached to it and commutation is achieved electronically. They are generally smaller but more expensive than conventional brushed type DC motors because they use "Hall effect" switches in the stator to produce the required stator field rotational sequence but they have better torque/speed characteristics, are more efficient and have a longer operating life than equivalent brushed types.
  • Servo Motor - This type of motor is basically a brushed DC motor with some form of positional feedback control connected to the rotor shaft. They are connected to and controlled by a PWM type controller and are mainly used in positional control systems and radio controlled models.
Normal DC motors have almost linear characteristics with their speed of rotation being determined by the applied DC voltage and their output torque being determined by the current flowing through the motor windings. The speed of rotation of any DC motor can be varied from a few revolutions per minute (rpm) to many thousands of revolutions per minute making them suitable for electronic, automotive or robotic applications. By connecting them to gearboxes or gear-trains their output speed can be decreased while at the same time increasing the torque output of the motor at a high speed.

The "Brushed" DC Motor

A conventional brushed DC Motor consist basically of two parts, the stationary body of the motor called the Stator and the inner part which rotates producing the movement called the Rotor or "Armature" for DC machines.
The motors wound stator is an electromagnet circuit which consists of electrical coils connected together in a circular configuration to produce the required North-pole then a South-pole then a North-pole etc, type stationary magnetic field system for rotation, unlike AC machines whose stator field continually rotates with the applied frequency. The current which flows within these field coils is known as the motor field current.
These electromagnetic coils which form the stator field can be electrically connected in series, parallel or both together (compound) with the motors armature. A series wound DC motor has its stator field windings connected in series with the armature. Likewise, a shunt wound DC motor has its stator field windings connected in parallel with the armature as shown.

Series and Shunt Connected DC Motor

Series and Shunt DC Motor

The rotor or armature of a DC machine consists of current carrying conductors connected together at one end to electrically isolated copper segments called the commutator. The commutator allows an electrical connection to be made via carbon brushes (hence the name "Brushed" motor) to an external power supply as the armature rotates.
The magnetic field setup by the rotor tries to align itself with the stationary stator field causing the rotor to rotate on its axis, but can not align itself due to commutation delays. The rotational speed of the motor is dependent on the strength of the rotors magnetic field and the more voltage that is applied to the motor the faster the rotor will rotate. By varying this applied DC voltage the rotational speed of the motor can also be varied.

Conventional (Brushed) DC Motor

Brushed DC Motor

Permanent magnet (PMDC) brushed motors are generally much smaller and cheaper than their equivalent wound stator type DC motor cousins as they have no field winding. In permanent magnet DC (PMDC) motors these field coils are replaced with strong rare earth (i.e. Samarium Cobolt, or Neodymium Iron Boron) type magnets which have very high magnetic energy fields. This gives them a much better linear speed/torque characteristic than the equivalent wound motors because of the permanent and sometimes very strong magnetic field, making them more suitable for use in models, robotics and servos.
Although DC brushed motors are very efficient and cheap, problems associated with the brushed DC motor is that sparking occurs under heavy load conditions between the two surfaces of the commutator and carbon brushes resulting in self generating heat, short life span and electrical noise due to sparking, which can damage any semiconductor switching device such as a MOSFET or transistor. To overcome these disadvantages, Brushless DC Motors were developed.

The "Brushless" DC Motor

The brushless DC motor (BDCM) is very similar to a permanent magnet DC motor, but does not have any brushes to replace or wear out due to commutator sparking. Therefore, little heat is generated in the rotor increasing the motors life. The design of the brushless motor eliminates the need for brushes by using a more complex drive circuit were the rotor magnetic field is a permanent magnet which is always in synchronisation with the stator field allows for a more precise speed and torque control. Then the construction of a brushless DC motor is very similar to the AC motor making it a true synchronous motor but one disadvantage is that it is more expensive than an equivalent "brushed" motor design.
The control of the brushless DC motors is very different from the normal brushed DC motor, in that it this type of motor incorporates some means to detect the rotors angular position (or magnetic poles) required to produce the feedback signals required to control the semiconductor switching devices. The most common position/pole sensor is the "Hall Effect Sensor", but some motors also use optical sensors.
Using Hall effect sensors, the polarity of the electromagnets is switched by the motor control drive circuitry. Then the motor can be easily synchronized to a digital clock signal, providing precise speed control. Brushless DC motors can be constructed to have, an external permanent magnet rotor and an internal electromagnet stator or an internal permanent magnet rotor and an external electromagnet stator.
Advantages of the Brushless DC Motor compared to its "brushed" cousin is higher efficiencies, high reliability, low electrical noise, good speed control and more importantly, no brushes or commutator to wear out producing a much higher speed. However their disadvantage is that they are more expensive and more complicated to control.

The DC Servo Motor

DC Servo motors are used in closed loop type applications were the position of the output motor shaft is fed back to the motor control circuit. Typical positional "Feedback" devices include Resolvers, Encoders and Potentiometers as used in radio control models such as airplanes and boats etc. A servo motor generally includes a built-in gearbox for speed reduction and is capable of delivering high torques directly. The output shaft of a servo motor does not rotate freely as do the shafts of DC motors because of the gearbox and feedback devices attached.

DC Servo Motor Block Diagram

DC Servo Motor

A servo motor consists of a DC motor, reduction gearbox, positional feedback device and some form of error correction. The speed or position is controlled in relation to a positional input signal or reference signal applied to the device.
RC Servo Motor
RC Servo Motor
The error detection amplifier looks at this input signal and compares it with the feedback signal from the motors output shaft and determines if the motor output shaft is in an error condition and, if so, the controller makes appropriate corrections either speeding up the motor or slowing it down. This response to the positional feedback device means that the servo motor operates within a "Closed Loop System".
As well as large industrial applications, servo motors are also used in small remote control models and robotics, with most servo motors being able to rotate up to about 180 degrees in both directions making them ideal for accurate angular positioning. However, these RC type servos are unable to continually rotate at high speed like conventional DC motors unless specially modified.
A servo motor consist of several devices in one package, the motor, gearbox, feedback device and error correction for controlling position, direction or speed. They are widley used in robotics and models as they are easily controlled using just three wires, PowerGround and Signal Control.

DC Motor Switching and Control

Small DC motors can be switched "On" or "Off" by means of switches, relays, transistors or mosfet circuits with the simplest form of motor control being "Linear" control. This type of circuit uses a bipolarTransistor as a Switch (A Darlington transistor may also be used were a higher current rating is required) to control the motor from a single power supply.
By varying the amount of base current flowing into the transistor the speed of the motor can be controlled for example, if the transistor is turned on "half way", then only half of the supply voltage goes to the motor. If the transistor is turned "fully ON" (saturated), then all of the supply voltage goes to the motor and it rotates faster. Then for this linear type of control, power is delivered constantly to the motor as shown below.

Unipolar Transistor Switch

Unipolar Transistor Switch
The simple switching circuit on the left, shows the circuit for a Uni-directional (one direction only) motor control circuit. A continuous logic "1" or logic "0" is applied to the input of the circuit to turn the motor "ON" (saturation) or "OFF" (cut-off) respectively.
A flywheel diode is connected across the motor terminals to protect the switching transistor or MOSFET from any back emf generated by the motor when the transistor turns the supply "OFF".
As well as the basic "ON/OFF" control the same circuit can also be used to control the motors rotational speed. By repeatedly switching the motor current "ON" and "OFF" at a high enough frequency, the speed of the motor can be varied between stand still (0 rpm) and full speed (100%). This is achieved by varying the proportion of "ON" time (tON) to the "OFF" time (tOFF) and this can be achieved using a process known as Pulse Width Modulation.

Pulse Width Speed Control

The rotational speed of a DC motor is directly proportional to the mean (average) value of its supply voltage and the higher this value, up to maximum allowed motor volts, the faster the motor will rotate. In other words more voltage more speed. By varying the ratio between the "ON" (tON) time and the "OFF" (tOFF) time durations, called the "Duty Ratio", "Mark/Space Ratio" or "Duty Cycle", the average value of the motor voltage and hence its rotational speed can be varied. For simple unipolar drives the duty ratioβ is given as:
Duty Cycle
and the mean DC output voltage fed to the motor is given as: Vmean = β x Vsupply. Then by varying the width of pulse a, the motor voltage and hence the power applied to the motor can be controlled and this type of control is called Pulse Width Modulation or PWM.
Another way of controlling the rotational speed of the motor is to vary the frequency (and hence the time period of the controlling voltage) while the "ON" and "OFF" duty ratio times are kept constant. This type of control is called Pulse Frequency Modulation or PFM. With pulse frequency modulation, the motor voltage is controlled by applying pulses of variable frequency for example, at a low frequency or with very few pulses the average voltage applied to the motor is low, and therefore the motor speed is slow. At a higher frequency or with many pulses, the average motor terminal voltage is increased and the motor speed will also increase.
Then, Transistors can be used to control the amount of power applied to a DC motor with the mode of operation being either "Linear" (varying motor voltage), "Pulse Width Modulation" (varying the width of the pulse) or "Pulse Frequency Modulation" (varying the frequency of the pulse).

H-bridge Motor Control

While controlling the speed of a DC motor with a single transistor has many advantages it also has one main disadvantage, the direction of rotation is always the same, its a "Uni-directional" circuit. In many applications we need to operate the motor in both directions forward and back. One very good way of achieving this is to connect the motor into a Transistor H-bridge circuit arrangement and this type of circuit will give us "Bi-directional" DC motor control as shown below.

Basic Bi-directional H-bridge Circuit

H-Bridge Circuit

The H-bridge circuit above, is so named because the basic configuration of the four switches, either electro-mechanical relays or transistors resembles that of the letter "H" with the motor positioned on the centre bar. The Transistor or MOSFET H-bridge is probably one of the most commonly used type of bi-directional DC motor control circuits. It uses "complementary transistor pairs" both NPN and PNP in each branch with the transistors being switched together in pairs to control the motor.
Control input A operates the motor in one direction ie, Forward rotation while input B operates the motor in the other direction ie, Reverse rotation. Then by switching the transistors "ON" or "OFF" in their "diagonal pairs" results in directional control of the motor.
For example, when transistor TR1 is "ON" and transistor TR2 is "OFF", point A is connected to the supply voltage (+Vcc) and if transistor TR3 is "OFF" and transistor TR4 is "ON" point B is connected to 0 volts (GND). Then the motor will rotate in one direction corresponding to motor terminal A being positive and motor terminal B being negative. If the switching states are reversed so that TR1 is "OFF", TR2 is "ON", TR3 is "ON" and TR4 is "OFF", the motor current will now flow in the opposite direction causing the motor to rotate in the opposite direction.
Then, by applying opposite logic levels "1" or "0" to the inputs A and B the motors rotational direction can be controlled as follows.

H-bridge Truth Table

Input AInput BMotor Function
TR1 and TR4TR2 and TR3
00Motor Stopped (OFF)
10Motor Rotates Forward
01Motor Rotates Reverse
It is important that no other combination of inputs are allowed as this may cause the power supply to be shorted out, ie both transistors, TR1 and TR2 switched "ON" at the same time, (fuse = bang!).
As with uni-directional DC motor control as seen above, the rotational speed of the motor can also be controlled using Pulse Width Modulation or PWM. Then by combining H-bridge switching with PWM control, both the direction and the speed of the motor can be accurately controlled. Commercial off the shelf decoder IC's such as the SN754410 Quad Half H-Bridge IC or the L298N which has 2 H-Bridges are available with all the necessary control and safety logic built in are specially designed for H-bridge bi-directional motor control circuits.

The Stepper Motor

Like the DC motor above, Stepper Motors are also electromechanical actuators that convert a pulsed digital input signal into a discrete (incremental) mechanical movement are used widely in industrial control applications. A stepper motor is a type of synchronous brushless motor in that it does not have an armature with a commutator and carbon brushes but has a rotor made up of many, some types have hundreds of permanent magnetic teeth and a stator with individual windings.
Stepper Motor
Stepper Motor
As it name implies, a stepper motor does not rotate in a continuous fashion like a conventional DC motor but moves in discrete "Steps" or "Increments", with the angle of each rotational movement or step dependant upon the number of stator poles and rotor teeth the stepper motor has.
Because of their discrete step operation, stepper motors can easily be rotated a finite fraction of a rotation at a time, such as 1.8, 3.6, 7.5 degrees etc. So for example, lets assume that a stepper motor completes one full revolution (360o in exactly 100 steps. Then the step angle for the motor is given as 360 degrees/100 steps = 3.6 degrees per step. This value is commonly known as the stepper motors Step Angle.
There are three basic types of stepper motor, Variable Reluctance,Permanent Magnet and Hybrid (a sort of combination of both). A Stepper Motor is particularly well suited to applications that require accurate positioning and repeatability with a fast response to starting, stopping, reversing and speed control and another key feature of the stepper motor, is its ability to hold the load steady once the require position is achieved.
Generally, stepper motors have an internal rotor with a large number of permanent magnet "teeth" with a number of electromagnet "teeth" mounted on to the stator. The stators electromagnets are polarized and depolarized sequentially, causing the rotor to rotate one "step" at a time.
Modern multi-pole, multi-teeth stepper motors are capable of accuracies of less than 0.9 degs per step (400 Pulses per Revolution) and are mainly used for highly accurate positioning systems like those used for magnetic-heads in floppy/hard disc drives, printers/plotters or robotic applications. The most commonly used stepper motor being the 200 step per revolution stepper motor. It has a 50 teeth rotor, 4-phase stator and a step angle of 1.8 degrees (360 degs/(50x4)).

Stepper Motor Construction and Control

Variable Reluctance Stepper Motor

In our simple example of a variable reluctance stepper motor above, the motor consists of a central rotor surrounded by four electromagnetic field coils labelled ABC and D. All the coils with the same letter are connected together so that energising, say coils marked A will cause the magnetic rotor to align itself with that set of coils. By applying power to each set of coils in turn the rotor can be made to rotate or "step" from one position to the next by an angle determined by its step angle construction, and by energising the coils in sequence the rotor will produce a rotary motion.
The stepper motor driver controls both the step angle and speed of the motor by energising the field coils in a set sequence for example, "ADCB, ADCB, ADCB, A..." etc, the rotor will rotate in one direction (forward) and by reversing the pulse sequence to "ABCD, ABCD, ABCD, A..." etc, the rotor will rotate in the opposite direction (reverse).
So in our simple example above, the stepper motor has four coils, making it a 4-phase motor, with the number of poles on the stator being eight (2 x 4) which are spaced at 45 degree intervals. The number of teeth on the rotor is six which are spaced 60 degrees apart. Then there are 24 (6 teeth x 4 coils) possible positions or "steps" for the rotor to complete one full revolution. Therefore, the step angle above is given as:   360o/24 = 15o.
Obviously, the more rotor teeth and or stator coils would result in more control and a finer step angle. Also by connecting the electrical coils of the motor in different configurations, Full, Half and micro-step angles are possible. However, to achieve micro-stepping, the stepper motor must be driven by a (quasi) sinusoidal current that is expensive to implement.
It is also possible to control the speed of rotation of a stepper motor by altering the time delay between the digital pulses applied to the coils (the frequency), the longer the delay the slower the speed for one complete revolution. By applying a fixed number of pulses to the motor, the motor shaft will rotate through a given angle and so there would be no need for any form of additional feedback because by counting the number of pulses given to the motor the final position of the rotor will be exactly known. This response to a set number of digital input pulses allows the stepper motor to operate in an "Open Loop System" making it both easier and cheaper to control.
For example, lets assume that our stepper motor above has a step angle of 3.6 degs per step. To rotate the motor through an angle of say 216 degrees and then stop again at the require position would only need a total of: 216 degrees/(3.6 degs/step) = 80 pulses applied to the stator coils.
There are many stepper motor controller IC's available which can control the step speed, speed of rotation and motors direction. One such controller IC is the SAA1027 which has all the necessary counter and code conversion built-in, and can automatically drive the 4 fully controlled bridge outputs to the motor in the correct sequence. The direction of rotation can also be selected along with single step mode or continuous (stepless) rotation in the selected direction, but this puts some burden on the controller. When using an 8-bit digital controller, 256 microsteps per step are also possible

SAA1027 Stepper Motor Control Chip

saa1027 stepper motor control chip