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RESONANT CIRCUITS
FILTERS NETWORK TRAINER
MODEL-COM306

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SIGMA TRAINERS
AHMEDABAD (INDIA)


INTRODUCTION
This trainer has been designed with a view to provide practical and experimental knowledge of various types
of filters & Resonance circuits on a SINGLE P.C.B. of size 12 "x 9".

SPECIFICATIONS
1.

Power supply requirement

2.

Built in IC based power supply.

3.

Filter Sections

:

230V AC, 50 Hz.

:

Low Pass filter
High Pass filter
Band Pass filter
Band Reject and Quartz filter
Series resonance
Parallel resonance
Quartz Filter

4.

All parts are soldered on single pin TAGS on single PCB of size 12" x 9" with complete circuit diagram
Screen-printed.

5.

Standard Accessories

:

1. A Training Manual.
2. Connecting Patch cords.

2


CHAPTER-1
THEORY OF FILTERS
Although there are a great many different types of filter, they really only fall into four main categories. These
are high pass, low pass, band pass, and notch types. There are many ways of achieving each type of filtering,
which is why there appears to be a bewildering variety of filters in use in modern linear circuits. In this chapter
we will consider circuits of all four types, and in most cases filters of various levels of performance will be
described so that you will (hopefully) be able to choose a filter configuration that precisely suits your needs.
(A) Passive Filters:The simplest type of filter is a high pass or low pass type that merely consists of one capacitor and one
resistor. These two types of filter are shown in Figure 1, and these give an ultimate roll-off rate of 6dB octave.
In other words, a doubling or halving of frequency (as appropriate) results in the output voltage being reduced
by 50%.

Fig. 1(a) Simple low pass filter

Fig.1 (b) Simple high pass-filter.

These circuits relay on the fact that the reactance of a capacitor decreases as frequency is increases, and this
simple principle is in fact used in all the filters that are described in this publication. If we take the low pass
filter first, at low frequencies C1 has a reactance which is high when compared with the resistance of R1, and
the
losses through R1 due to a straight forward potential divider action are therefore very small. At higher
frequencies the reactance of C1 falls and eventually reaches a point where it is equal to the resistance of R1,
and at this point the losses through the circuit are 6dB. Doubling the input frequency results in a halving of the

reactance of C1, and the losses through the filter are doubled to 12dB. Further doubling of the input frequency
causes the reactance of C1 to half, and the losses through the circuit to be doubled (or increased by 6dB in other
words). Thus the ultimate 6dB per octave attenuation rate is achieved. Note though that the roll-off rate is lower
than this at frequencies below the -6dB point, and this type of filter should therefore be said to have an ultimate
attenuation rate of 6dB per octave rather than just a 6dB per octave attenuation rate.
The high pass filter works in very much the same way, but it is at high frequencies where the reactance of C1
is low that the circuit produces low losses, and at low frequencies where the reactance of C1 is high in relation
to that of R1 that the circuit gives the 6dB per octave roll-off.

3


The values shown in Figure 1 gives a -6dB point at approximately 1Khz, but the -6dB frequency can be
altered by changing the value of C1 or that of R1, or both. Changes in value give an inversely proportional
change in the -6dB frequency. For instance, making R1 1k and C1 3n3 would produce a 6dB point at
approximately 100Khz.
Circuits of this type look deceptively simple, and this is due to the fact that the cut off frequency obtained
and the roll-off rate of the filter are largely dependent on the source and load impedances at the input and
output of the filter. For the filter to achieve its theoretical level of performance it must be fed from a source
impedance that is very low and have a load impedance that is very high. If we take a couple of extreme
examples to demonstrate this point, assume that the circuit of Figure 1(a) is fed from a source impedance of
100k, this source impedance is effectively added to R1 to give a value here of 110k, which would give 1 -6dB
point of less than 100Hz instead of about 1Khz. If the circuit is fed from a low source impedance but a load
impedance of 1K is across the output, there will obviously be losses of over 20dB due to the potential divider
action produced by R1 and the load impedance. C1 would start to significantly increase the attenuation provided
by the circuit only when its reactance became comparable to and less than the load impedance. This would be at
a frequency of about 10Khz and upwards, and would again seriously effect the performance of the circuit.
In practice circuits of this type are quite often used, but more common practice is a simple low pass filter in
the form of a capacitor connected across the collector load resistor of a common emitter amplifier. Here the cutoff frequency would be determined by the value given to the filter capacitor and the combined impedance of the
load resistance and the input impedance of the circuit driven by the amplifier (these two impedances effectively

being connected in parallel with one another). Low pass filtering is sometimes added to an operational amplifier
circuit. Here the filter capacitor would be added in parallel with R2 so that the amplifier would have increased
negative feedback and reduced voltage gain at high frequencies where the filter capacitor would effectively
reduce the value of R2 by a substantial amount. The cut-off frequency would then be determined simply by the
values of R2 and the filter capacitor.
A high pass filter is often produced by simply using a low value coupling capacitor between two stages so that
in effect C1 is the coupling capacitor and R1 is the input impedance of the stage to which it is coupling the
signal.
Active Filters :
Where a filter having an attenuation rate of more than 6dB per octave is required it is normal these days to
use an active circuit. While on the face of it there is no reason why two simple filters of the type shown in
Figure 1(a) or (b) should not be connected in series to give a 12dB per octave roll-off rate, in practice loading
of the first filter section on the second tends to give problems. A passive 12dB per octave filter tends to have a
rather low initial roll-off rate which can result in wanted signals at frequencies just below the cut-off frequency
being significantly attenuated, or signals at frequencies not far above the cut-off frequency receiving little
attenuation, or a combination of the two, depending on what compromise is used for the cut-off frequency. We
are talking in terms of a low pass filter here, but the situation is essentially the same for a high pass type. It
then becomes wanted signals just above the cut-off frequency that are attenuated, and (or) signals at frequencies
just below the cut-off frequency that receive little attenuation.

4


QUARTZ CRYSTAL OVERVIEW
Quartz crystals use the piezo electric effect to convert the incoming electrical impulses into mechanical
vibrations. These vibrations are affected by the mechanical resonance of the crystal, and as the piezo electric
effect operates in both directions, the mechanical resonance affect the electrical stimuli, being reflected back
into the electrical circuit.
The levels of Q that can be achieved using quartz crystals range into figures well over 10 000. Values of
100 000 are widely used in filters and values can sometimes reach 500 000. By utilizing this level of

performance, quartz crystal filters can achieve very high levels of performance. This can be reflected in the
crystal filters very narrow filter bandwidths and sharp cut-off curves.
Quartz crystal cuts
When manufacturing the quartz crystal blanks used to make the electronic components used in filters, the angle
at which these blanks are cut from the unprepared crystal, have a major bearing on the properties. A form of cut
known as the AT cut is used for most radio applications. This provides the optimum set of parameters for most
radio applications. The size of the crystal blank using this cut is such that it is sufficiently robust to withstand
the manufacturing process without a high level of failures and rejects, and to withstand the vibration that is
likely to be expected in use. Additionally the level of spurious responses is low. A further advantage is that the
temperature stability is high. The final angle of the cut can be adjusted to ensure that the temperature
characteristic is optimum for the particular application for which it is intended. Even a difference of 2 minutes
of arc can be detected, although the normal manufacturing spread is around 3 minutes of arc.
In addition to this the cut of the quartz crystal governs the way in which it vibrates. As there are several modes
in which a crystal can vibrate it is necessary to choose a cut in which unwanted modes are not easy to excite. If
they are present then they will be seen as spurious responses in the crystal filter.
Filter parameters
There are two main areas of interest for a filter, the pass band where it accepts signals and allows them through,
and the stop band where it rejects them. In an ideal world a filter would have a response something like that
shown below. Here it can be seen that there is an immediate transition between the pass band and the stop band.
Also in the pass band the filter does not introduce any loss and in the stop band no signal is allowed through.
The response of an ideal filter
In reality it is not possible to realise a filter with these characteristics and a typical response more like that
shown in Figure 3. It is fairly obvious from the diagram that there are a number of differences. The first is that
there is some loss in the pass band. Secondly the response does not fall away infinitely fast. Thirdly the stop
band attenuation is not infinite, even though it is very large. Finally it will be noticed that there is some in band
ripple.

5

Typical response of a real filter
In most filters the attenuation in the pass band is normally relatively small. For a typical crystal filter figures of
2 - 3 dB are fairly typical. However it is found that very narrow band filters like those used for Morse reception
may be higher than this. Fortunately it is quite easy to counteract this loss simply by adding a little extra
amplification in the intermediate frequency stages and this factor is not quoted as part of the receiver
specification.
It can be seen that the filter response does not fall away infinitely fast, and it is necessary to define the points
between which the pass band lies. For receivers the pass band is taken to be the bandwidth between the points
where the response has fallen by 6 dB, i.e. where it is 6 dB down or -6 dB.
A stop band is also defined. For most receiver filters this is taken to start at the point where the response has
fallen by 60 dB, although the specification for the filter should be checked this as some filters may not be as
good. Sometimes a filter may have the stop band defined for a 50 dB attenuation rather than 60 dB.
Shape factor
It can be seen that it is very important for the filter to achieve its final level of rejection as quickly as possible
once outside the pass band. In other words the response should fall as quickly as possible. To put a measure on
this, a figure known as the shape factor is used. This is simply a ratio of the bandwidths of the pass band and
the stop band. Thus a filter with a pass band of 3 kHz at -6dB and a figure of 6 kHz at -60 dB for the stop band
would have a shape factor of 2:1. For this figure to have real meaning the two attenuation figures should also be
quoted. As a result the full shape factor specification should be 2:1 at 6/60 dB.
Filter design parameters
When a quartz crystal bandpass filter is designed factors such as the input and output impedance as well as
bandwidth, crystal Q and many other factors need to be taken into account.
Some of the chief factors are obviously the bandwidth, shape fact, and ultimate cutoff. Although it is very much
a simplification, these factors are dependent upon the number of poles (equivalent to the number of crystals),
their Q value, and their individual frequencies.
Further factors such as the maximum bandwidth that can be achieved is controlled by the filter impedance and
also the spurious responses that are present in the individual quartz crystal elements. The location of the
important responses for quartz crystal band pass filters can be controlled by the size of the plates deposited onto
the crystals. By making them smaller the responses also become less critical. The down side of this is that the
impedance of the overall quartz crystal filter rises. This means that the crystal filter will need impedance

transformers at the input and the output. This obviously needs to be avoided if at all possible, but for wide band
filters it is often the only option.
6


CHAPTER-2
THEORY OF RESONANCE CIRCUITS
SERIES RESONANCE

7


8


9


10


PARALLEL RESONANCE

11


12


13

14


CHAPTER-3
CIRCUITS OF FILTERS
The Active Filter circuit trainer consists of following sections.
1.
2.
3.
4.
5.
6.

Low Pass Filter section
High Pass Filter section
Band Pass Filter section
Band Reject Filter section
Quartz Filter Section
Power supply.

(1) Low Pass Filter:With an active filter it is possible to obtain a flat response almost to the frequency where the 12dB per octave
roll-off rate commences.
The low pass filter section uses IC 356 as a unity gain buffer amplifier. The cut-off frequency is determined
by the values of R3, R4, C1 and C2, with a -3dB point at about 1Khz with the specified values. However, by
changing the values of C1 and C2 it is possible to alter the cut-off frequency to practically any desired figure
from a few Hertz to about 100Khz. Changes in the values of C1 and C2 produce an inversely proportional shift
in the cut-off frequency. For example, a scratch filter with a cut-off frequency of 5Khz could be produced by
reducing C1 to 1nF (C1') and C2 to 470pf (C2'). Obviously where exactly the required values are not available,

it is necessary to use the nearest preferred values. It is important to keep C1 at a value, which is double or
slightly more than double the value of C2. If C1 is slightly lower in value than this the initial roll-off rate of the
filter will be less than optimum, whereas making C1 somewhat too high in value will produce a peak in the
response of the filter just below the cut-off frequency.
R1 and R2 are used to bias IC1, and the bias current flows to IC via filter resistors R3 and R4. These are
placed ahead of the filter resistors so that they do not shunt C2, which would be the case if they were connected
direct at the input to IC. The input impedance of the circuit is about 5 kilohms.
(2) High Pass Filter:The High pass filter section uses IC 356 as a unity gain buffer and has active 12dB per octave filtering. This
is basically the same as the low pass circuit just described but the resistive and capacitive filter elements have
been transposed. R2 and R3 bias IC, and the combined (parallel) impedance of these acts as one of the resistive
filter elements.
The values shown give a -3dB point at approximately 1Khz, but it is again possible to modify the cut-off
frequency by altering the values of the capacitive elements of the filter (C1 and C2). Also as before, changes in
value give an inversely proportional shift in the cut-off frequency. Thus, for example, the circuit could operate
as a tumble filter in a huffy system with a cut-off frequency of around 50Hz by giving C1 and C2 a value of
470nF (C1' and C2'). Keep these two components at the same value or the performance of the filter will be
adversely affected.
(3) Band Pass Filter:A band pass filter, as its name suggests, permits frequencies within a narrow band to pass with little
attenuation while providing high losses at all other frequencies. A band pass filter can be produced using the
high pass and low pass filter circuits described earlier, and this method of band pass filtering is used in some
applications. For example, suppose an audio filter for some piece of communications equipment is required, and
it must have a pass band which extends from 250Hz to 3Khz. This could be achieved using a high pass filter
having a cut-off frequency of 250Hz and a low pass filter having a 3Khz cut-off frequency with the two filters
simply being used in series. It does not really matter too mush which filter is used to process the signal first,
although a marginally better signal-to-noise ratio will be obtained using the high pass filter at the input and the
low pass type at the.
15


The method described above is most useful where a flat response over a range of frequencies is required,

rather than a filter which is designed to pick out a signal at a certain frequency and attenuate other signals.
Where a very narrow bandwidth is required it is better to use a simple band pass filter of the type shown in
Figure. The specified values give a Centre frequency of approximately 1Khz, but this frequency can be made
anything from a few Hertz to about 100Khz by giving C1 and C2 suitable values.
A Voltage gain of a little over two times is provided at the Centre of the filters response, and the response is
not particularly sharp with the -6dB points at approximately 500Hz and 2Khz. However, the Q of the circuit can
be boosted considerably by reducing R1 to 1k8 and increasing R2 to 180k. This gives a relative attenuation of
nearly -20dB at 500Hz and 2Khz, and the voltage gain of the circuit is boosted to about 34dB (50 times).
Obviously an attenuator can be used at the input or output of the filter if this voltage is not needed.
The circuit must be fed from a low impedance source since the output impedance of the preceding stage is
effectively in series with R1 and will reduce the operating frequency of the filter. If necessary a buffer stage
(such as the one shown in Figure 4) must be added at the input. The filter can be tuned over a small range of
frequencies by replacing R1 or R2 with a variable resistor and fixed resistor in series, but the bandwidth of the
circuit will change somewhat as the filter is tuned up and down in frequency (which is why only a limited
tuning range is practical).
(4) Band Reject Filter:
The purpose of a Band reject filter is to let most frequencies pass with little hindrance, but to provide a high
level of attenuation over a narrow band of frequencies. Figure shows the circuit diagram of a notch filter of the
twin T type, and this is really just a passive filter with IC1 being used as a buffer stage at the output of the
circuit to ensure that there is minimal loading on the filter proper. R1 and R2 are used to bias IC1, and C2 is a
DC blocking capacitor. R3, R4, VR1 and C2 to C5 are the filter components. C4 and C5 are connected in
parallel to give a capacitance of 20nF since it is unlikely that a component of this value will be available. VR1
could replaced with a 9Kfixed resistor (which would need to consist of two 18k component connected in
parallel), but in order to obtain a deep notch it is better to use a variable resistor here so that it can be adjusted
to optimize the performance of the filter. This type of circuit can provide a very high level of attenuation at the
Center of the notch with 80dB being readily obtainable, although VR1 must be adjusted very precisely in order
to obtain best results from this circuit.
(5) Quartz Filter:
Quartz crystal filters provide an effective means of realizing filter solutions for many high performance
radio frequency filter applications. The high Q values that quartz crystals possess can be utilized in bandpass

filters for use in areas such as radio receivers. These quartz crystal filters are far superior to those that could be
manufactured using LC components. Although they are more costly than LC filters, the performance of a crystal
bandpass filter is still superior and in terms of cost they actually provide excellent value for money.
Today crystal filters can be designed with pass bands ranging from frequencies in the kilohertz region
up to many Megahertz - with the latest technology this can rise to 100 MHz and more. However for the best
performance and lowest costs the pass band of the filter is generally kept to below about 30 MHz or so.
(6) Power supply section:The +15 V regulated power supply is required to operate this trainer.
IC 7815 three terminal regulator is used for regulation. This IC is supplied dc input voltages by bridge
rectifier consisting of D1-D4 and C1. The capacitors at each input and each output are for filtering purpose.
SW1 is main AC ON/OFF Switch.
*************
16


2nd order LPF (Fig.2)

Step 1

(1) Low Pass Filter:
1.

Step 2

2.

EXPERIMENTS

vin=Vipsin(2*pi*f*t)=1.4sin(2*pi*f*t) (V)

Connect 2.8Vpp Sine wave signal from function generator at the input terminals of Low pass filter.

Connect CRO channel 1 at input of Low pass filter. Connect CRO channel 2 at the output terminals of
Low pass filter.

Osilloscope channel A= CRO channel 1

vout=1.sin(2*pi*f*t) (V)
Start varying frequency of input sine wave signal from 0 Hz onwards.
Observe input and output signals on CRO. The output will be same as input in starting. After that it will
reduce. Observe the frequency reading of sinewave input when output at CRO channel 2 becomes 2Vpp.
This is a cut off frequency of Low pass filter. This will be approx. 1 KHz..

2nd order HPF (Fig.3) Vipp=2.8 (V);Vary fi--> Vopp=Vipp/1.414=2V (Vop=1V) Av=
(2) High Pass Filter:
(Vopp/Vipp)=0.7 times-->-3dB-->fi=fc
1.

Connect 2.8Vpp Sine wave signal from function generator at the input terminals of High pass filter.
Connect CRO channel 1 at input of High pass filter. Connect CRO channel 2 at the output terminals of
High pass filter.

2.

Start varying frequency of input sinewave signal from 0 Hz onwards.
Observe input and output signals on CRO. The output will be zero in the starting. After that it will
increase. Observe the frequency
reading of sinewave input when output at CRO channel 2 becomes
2Vpp. This is a cut off frequency of High pass filter. This will be approx. 2 KHz.

2nd order BPF (Fig.4)
(3) Band Pass Filter:

1.

Connect 2.8Vpp Sine wave signal from function generator at the input terminals of Band pass filter.
Connect CRO channel 1 at input of Band pass filter. Connect CRO channel 2 at the output terminals
of Band pass filter.

2.

Start varying frequency of input sine wave signal from 0 Hz onwards.
Observe input and output signals on CRO. The output will be zero in the starting. After that it will
increase and once again it will decrease. Observe the frequency reading of sinewave input when output
at CRO channel 2 becomes 2Vpp. There will be two positions where 2Vpp level occurs. These
frequencies will be 400 Hz and 6KHz approx. Center frequency between these frequencies will be 3KHz
approx.
(4) Band Reject Filter:

BRF (Fig.5)

1.

Connect 2.8Vpp Sine wave signal from function generator at the input terminals of Notch filter.
Connect CRO channel 1 at input of Notch filter. Connect CRO channel 2 at the output terminals of
Notch filter.

2.

Start varying frequency of input sinewave signal from 0 Hz onwards.
Observe input and output signals on CRO. The output will be same as input in the starting. After that
it will decrease and once again it will increase. Observe the frequency reading of sinewave input
when output at CRO channel 2 becomes minimum. This will be approx.1200Hz to 3KHz.

(5) Quartz Filter:

1.

Connect 2.8Vpp Sine wave signal from function generator at the input terminals of Crystal filter.

2.

Keep both potentiometers fully clockwise. Keep tuning condenser at mid range.

3.

Connect CRO channel 1 at input of Crystal filter. Connect CRO channel 2 at the output terminals.
17


2.

Start varying frequency of input sine wave signal from 0 Hz onwards.
Observe input and output signals on CRO. The output will be low in starting. After that it will increase
when frequency become 400Khz. At frequency 455 KHZ, the output will be maximum. Then it will again
reduce. Observe the frequencies reading of sinewave input when output at CRO channel 2 becomes 2Vpp
below and above 455KHz frequency. The difference between these frequencies is known as bandwidth of
crystal filter. These will be approx. 4 to 10KHz and can be changed by varying pots and capacitor.
(6) Series Resonance:
1.

Connect circuit as shown in figure.

2.

Connect 5Vpp Sine wave signal from function generator at the input terminals.

3.

Connect CRO Channel -1 across capacitor and Channel 2 across inductor.

4.

Vary input frequency from 10 Hz to 1Mhz. Note the frequency when amplitude of both waveforms
become same i.e. resonance occurs. Also measure the ac voltage across capacitor and inductor and make
conclusion. It will be approx. 30KHz for C1=820 pf and 80KHz for C2=2200pf.

(7) Parallel Resonance:
5.

Connect circuit as shown in figure.

6.

Connect 2Vpp Sine wave signal from function generator at the input terminals.

7.

Connect two AC ammeter to measure IL and IC currents.

8.

Vary input frequency from 10 Hz to 1Mhz. Note the frequency when value of both currents become
same i.e. resonance occurs.

It will be approx. 130 KHz for C1=820 pf and 140KHz for C2=2200pf.

Conclusion: Different types of filters & resonance circuits understood.
***********

18


1

pasive HPF

XFG
XSC
XBP

19

AG

6

1

2

3

12V

vo(t)=sin(2*pi*fi*t) V
fi=fc cutt-off frequency

vi(t)=1.4sin(2*pi*fi*t) V

AC mode

7
5

AC mode

4

8