![IF transformer](https://upload.wikimedia.org/wikipedia/commons/9/97/IF_transformer.JPG)
A double-tuned amplifier is a
tuned amplifier
A tuned amplifier is an electronic amplifier which includes bandpass filtering components within the amplifier circuitry. They are widely used in a variety of wireless applications.
Schemes
There are several tuning schemes in use,
* Stagger ...
with
transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
coupling between the amplifier stages in which the
inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
s of both the primary and secondary
winding
An electromagnetic coil is an electrical conductor such as a wire in the shape of a coil (spiral or helix). Electromagnetic coils are used in electrical engineering, in applications where electric currents interact with magnetic fields, in de ...
s are tuned separately with a
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
across each. The scheme results in a wider
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
and steeper
skirts
A skirt is the lower part of a dress or a separate outer garment that covers a person from the waist downwards.
At its simplest, a skirt can be a draped garment made out of a single piece of fabric (such as pareos). However, most skirts are fi ...
than a single
tuned circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can ac ...
would achieve.
There is a critical value of transformer
coupling coefficient at which the
frequency response
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of sy ...
of the amplifier is
maximally flat in the
passband
A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
and the
gain
Gain or GAIN may refer to:
Science and technology
* Gain (electronics), an electronics and signal processing term
* Antenna gain
* Gain (laser), the amplification involved in laser emission
* Gain (projection screens)
* Information gain in de ...
is maximum at the
resonant frequency
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
. Designs frequently use a coupling greater than this (over-coupling) in order to achieve an even wider bandwidth at the expense of a small loss of gain in the centre of the passband.
Cascading multiple stages of double-tuned amplifiers results in a reduction of the bandwidth of the overall amplifier. Two stages of double-tuned amplifier have 80% of the bandwidth of a single stage. An alternative to double tuning that avoids this loss of bandwidth is
staggered tuning
Staggered tuning is a technique used in the design of multi-stage tuned amplifiers whereby each stage is tuned to a slightly different frequency. In comparison to synchronous tuning (where each stage is tuned identically) it produces a wider Band ...
. Stagger-tuned amplifiers can be designed to a prescribed bandwidth that is greater than the bandwidth of any single stage. However, staggered tuning requires more stages and has lower gain than double tuning.
Typical circuit
![Double tuned amplifier](https://upload.wikimedia.org/wikipedia/commons/1/17/Double_tuned_amplifier.svg)
The circuit shown consists of two stages of
amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the v ...
in
common emitter
In electronics, a common-emitter amplifier is one of three basic single-stage bipolar-junction-transistor (BJT) amplifier topologies, typically used as a voltage amplifier. It offers high current gain (typically 200), medium input resistance a ...
topology. The
bias
Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, ...
resistors all serve their usual functions. The input of the first stage is
coupled
''Coupled'' is an American dating game show that aired on Fox from May 17 to August 2, 2016. It was hosted by television personality, Terrence J and created by Mark Burnett, of '' Survivor'', ''The Apprentice'', '' Are You Smarter Than a 5th G ...
in the conventional way with a series
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
to avoid affecting the bias. However, the collector load consists of a
transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
which serves as the inter-stage coupling instead of capacitors. The windings of the transformer have
inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
. Capacitors placed across the transformer windings form
resonant circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can ac ...
s which provide the tuning of the amplifier.
A further detail that may be seen in this kind of amplifier is the presence of
taps on the transformer windings. These are used for the input and output connections of the transformer rather than the top of the windings. This is done for
impedance matching
In electronics, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize signal ...
purposes;
bipolar junction transistor
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar ...
amplifiers (the kind shown in the circuit) have a quite high output
impedance and a quite low input impedance. This problem can be avoided by using
MOSFET
The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
s which have a very high input impedance.
The capacitors connected between the bottom of the transformer secondary windings and ground do not form part of the tuning. Rather, their purpose is to
decouple the transistor bias
resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
s from the
AC circuit.
Properties
Double tuning, as compared to single tuning, has the effect of widening the bandwidth of the amplifier and steepening the
skirt
A skirt is the lower part of a dress or a separate outer garment that covers a person from the waist downwards.
At its simplest, a skirt can be a draped garment made out of a single piece of fabric (such as pareos). However, most skirts are fi ...
of the response. Tuning both sides of the transformer forms a pair of
coupled resonators which is the source of the increased bandwidth. The gain of the amplifier is a function of the
coupling coefficient, ''k'', which is related to the
mutual inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of th ...
, ''M'', and the primary and secondary winding
inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
s, ''L''
p and ''L''
s respectively, by
:
There is a critical value of coupling at which the gain of the amplifier is a maximum at resonance. Below this critical value, there is a single peak in the frequency response with the amplitude peaking at resonance and the peak decreasing as ''k'' decreases. Such a response is said to be undercoupled, At values of ''k'' above critical coupling the response starts to split into two peaks. These peaks become narrower and further apart as ''k'' increases and the gap between them (centred on the resonant frequency) becomes progressively deeper. Such a response is said to be overcoupled.
A critically coupled amplifier has a response that is
maximally flat. This response can also be achieved without transformers with two stages of a
stagger-tuned amplifier. Unlike staggered tuning, double tuning usually tunes both resonators to the same
resonant frequency
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
. However, a designer might choose to design an overcoupled amplifier in order to achieve a wider bandwidth at the expense of a small dip (typically to maximize the bandwidth) in the centre of the frequency response.
Like
synchronous tuning, adding more stages of double-tuned amplifiers has the effect of reducing the bandwidth. The bandwidth of ''n'' identical stages, as a fraction of the bandwidth of a single stage, is given approximately by,
:
This expression applies only to small fractional bandwidths.
Analysis
The circuit can be represented in a more generic way by replacing the amplifiers with a generalised
transconductance Transconductance (for transfer conductance), also infrequently called mutual conductance, is the electrical characteristic relating the current through the output of a device to the voltage across the input of a device. Conductance is the reciproca ...
amplifier as shown.
![Doubler tuned amplifier generic](https://upload.wikimedia.org/wikipedia/commons/4/4c/Doubler_tuned_amplifier_generic.svg)
:where (omitting the stage number suffixes),
:''g''
m is the transconductance of the amplifiers
:''G''
o is the output conductance of the amplifiers
:''G''
i is the input conductance of the amplifiers.
Typically, a design will make the resonant frequencies and ''Q''s on the primary and secondary sides identical, such that,
:
:and,
:
:where ''ω''
0 is the resonant frequency expressed in units of
angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
and the subscripts p and s refer respectively to components on the primary and secondary side of the transformer.
Stage gain
With the above assumptions, the voltage gain, ''A'' of one stage of the amplifier can be expressed as
:
:where
:
is the
imaginary unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...
,
:
:is the maximum gain deliverable by the stage, and
:
:is the frequency expressed as the fractional frequency deviation from the resonant frequency.
Peak frequency
With less than critical coupling, there is one peak in the response occurring at resonance. Above critical coupling, there are two peaks at frequencies given by
:
:where ''δ''
L and ''δ''
H are respectively the low and high frequencies of the peaks expressed as fractional deviation.
With critical coupling or above, the peaks reach the maximum gain available from the amplifier.
Critical coupling
Critical coupling occurs when the two peaks just coincide. That is, when
:
or
:
[Bakshi & Godse, pp. 5.20–5.26 (for entire analysis section)]
References
Bibliography
* Bakshi, Uday A.; Godse, Atul P., ''Electronic Circuit Analysis'', Technical Publications, 2009 .
* Bhargava, N. N.; Gupta, S. C.; Kulshreshtha D. C., ''Basic Electronics and Linear Circuits'', Tata McGraw-Hill, 1984 .
* Chattopadhyay, D., ''Electronics: Fundamentals and Applications'', New Age International, 2006 .
* Gulati, R. R., ''Monochrome and Colour Television'', New Age International, 2007 .
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