Download Filter Types

The following describes filter types, what they do and how they
perform. Along with definitions and detailed graphs, we are
hopeful this information is both useful and informative.
Filter Types
Monolithic Crystal Filters
2 Quartz resonator internally coupled utilizing piezoelectric
effect.
Discrete Crystal Filter
Single quartz resonator with external
components utilizing the piezoelectric effect.
Notch filters
Crystal or Discrete component filter that passes
all frequencies except those in a stop band centered on a center
frequency.
High Pass Filters
Discrete component filter that passes high
frequency but alternates frequencies lower then the cut off
frequency.
Low Pass Filters
Discrete component filter that passes low
frequency signals but alternates signals with frequencies higher
then the cut off frequency.
Filter Designs
Chebyshev
The transfer function of the filter is derived from a
chebychev equal ripple function in the passband only. These
filters offer performance between that of Elliptic function filters
and Butterworth filters. For the majority of applications, this is the
preferred filter type since they offer improved selectivity, and the
networks obtained by this approximation are the most easily
realized.
Butterworth
The transfer function of the filter offers maximally flat
amplitude. Selectivity is better then Gaussian or Bessel filters,
but at the expense of delay and phase linearity. For most
bandpass designs, the VSWR at center frequency is extremely
good. Butterworth filters are usually the least sensitive to
changes in element values.
Bessel/Linear Phase
The transfer function of the filter is derived
from a Bessel polynomial. It produces filter with a flat delay
around center frequency. The more poles used, the wider the flat
region extends. The roll-off rate is poor. This type of filter is close
to a Gaussian filter. It has poor VSWR and loses its maximally
flat delay properties at wider bandwidths.
Elliptic
The passband ripple is similar to the Chebyshev but with greatly
improved stopband selectivity due to the addition of finite
attenuation peaks. The network complexity is increased over the
Butterworth or Chebyshev, but still yields practical realizations
over nearly the entire operating region.
Gaussian
The transfer function of the filter is derived from a Gaussian
function. The step and impulse response of a Gaussian filter has
zero overshoot. Rise times and delay are lowest of the traditional
transfer functions. These characteristics are obtained at the
expensive of poor selectivity, high element sensitivity, and a very
wide spread of element values. Gaussian filter is very similar to
the Bessel except that the delay has a slight “hump” at center
frequency and the rate of roll-off is slower. Because of the delay
response, the ringing characteristics are better then the Bessel.
Realization restrictions also apply to these filters.
Gaussian to 6 (or 12) dB– This approximation has a passband
response that follows the Gaussian shape and, at either the 6 or
12 dB point, the response changes and follows the Butterworth
characteristic. The phase, or delay, response is somewhat
improved over a strict Butterworth and the attenuation is better
than the pure Gaussian and so it is a true compromise type
of approximation, as with all of the filters where there is an
attempt to control the phase response, the realization becomes
more difficult and so its operating region is slightly restricted.
Typical Filter Eagleware Simulation
Discrete Crystal Filter
Typical Filter Eagleware Simulation
Bandpass LC Filter
Definitions
Center Frequency / Nominal Frequency
Center frequency is a given frequency in the specification, to
which other frequencies may be referred, while nominal
frequency is the nominal value of center frequency and
is used as the reference frequency for specifying relative levels
of attenuation. In bandpass and bandstop filters Fon denotes the
nominal center frequency; Fo denotes the actual or measured
center frequency of an individual filter and is usually defined
as:
Fo=(f1 x fu)1/2
Where f1 and fu are measured lower and upper passband limits,
usually the 3 dB attenuation frequencies. Sometimes it is more
convenient to specify frequency relative to the actual or
measured filter center frequency. The value of Fo will, of course,
vary from unit to unit within the same unit as function of
temperature and time. Therefore, there must be a tolerance
associated with Fo, making allowance for temperature, aging,
and manufacturing tolerances.
Passband, Stopband & Bandwidth
Passband is the frequency range in which a filter is intended to
pass signals. It is expressed as a range of frequencies
attenuated less than the specified value, typically specified at 3
db
Stopband is a band of frequencies in which the relative
attenuation of a filter is equal or greater then specified values. It
is expressed as a range of frequencies attenuated by more than
some specified minimum, such as 60 dB.
For a bandpass or band stop filter, the width (frequency
difference) between lower and upper points having a specified
attenuation, such as the 3 dB bandwidth or the 80 dB bandwidth.
For a lowpass filter, bandwidth is simply the frequency at which
the attenuation has the specified value.
Ripple / Passband Ripple
Generally referring to the wavelike variations in the amplitude
response of a filter with frequency. Ideal Chebychev and elliptic
function filters, for example, have equal-ripple characteristics,
which means that the differences in peaks and valleys of the
amplitude response in the pass band are equal. Butterworth,
Gaussian, and Bessel functions, on the other hand have no
ripple, Ripple is usually measured in dB. The pass band ripple is
defined as the difference between the maximum and minimum
attenuations within a pass band.
Shape Factor
Shape factor is the ration of the stopband bandwidth to the
passband bandwidth, typically the ratio of 60 dB bandwidth to
the 3 dB bandwidth. It is a critical parameter that determines the
number of poles and complexity required to meet the
specification.
Insertion Loss
The frequency response of filters is always considered as
relative to the attenuation occurring at a particular reference. The
actual attenuation at this reference is commonly called insertion
loss. It is referenced at the minimum attenuation point within the
pass band. Insertion loss can be defined as the logarithmic ratio
of the power delivered to the load impedance before insertion of
the filter to the power delivered to the load impedance after
insertion of the filter. In other words, it is the decrease in power
delivered to the load when a filter is inserted between the source
and the load. The insertion loss is given by:
ILdB = 10log(PL1/PL2)
Where PL1 is the power to the load with filter bypasses and PL2
is the out put power with filter inserted into the circuit. The
equation above can also be expressed in terms of a voltage ratio
as:
ILdB = 20log(VL1/VL2)
This allows insertion loss to be measured directly in terms of
output voltage.
Insertion Loss Linearity
The insertion loss of a filter may change with drive level. At high
power levels. Quartz resonators become non-linear causing the
filter loss to increase, and this phenomenon is primarily
determined by properties of the quartz , not by processing of the
filters.
However, at low drive levels resonator processing becomes
critical in maintaining constant insertion loss. With the application
of proper design, stringent processing and rigid controls, filters
have been being produced with no more than ±0.005 dB change
in insertion loss for a 40 dB Change in drive level.
Spurious Responses
All resonators, whether they are LC tuned circuits, cavity
resonators or crystal resonators have unwanted resonance
modes. Quartz crystals have anharmonic resonance normally
occurring just above the desired resonance as well as nearharmonic overtone responses.
Consequently, almost all crystal filters will exhibit unwanted
responses in their amplitude and phase characteristics. The
deviations are often, but not always, of narrow bandwidth.
Normally they occur in the filter stopband and appear as narrow,
unwanted regions of reduced attenuation. Spurious response
usually appears at a higher frequency than the center frequency.
Occasionally in wider bandwidth filters a spurious response may
occur in the filter passband, causing undesirable ripple.
The AT-cut crystal resonator, which is most commonly used for
filters, has a family of unwanted anharmonic responses at
frequencies slightly above the desired resonance and harmonic
(overtone) responses at approximately odd integer multiples of
the fundamental resonance. The location of the overtones and
the major anharmonics can be calculated in advance., The
overtone responses can be suppressed by additional LC filtering
which, given adequate package dimensions, can be
accommodated inside the filter package if required.
The near-by enharmonic responses cannot normally be
suppressed by LC filtering. Here suppression of spurious
responses is accomplished by a combination of resonator
design, resonator processing and filter circuit design. As the
crystal resonator electrode area is increased, more unwanted
anharmonic responses will be excited (assuming a constant
operation frequency) and the motional inductance will
decrease. In order to reduce insertion loss and/or retain a narrow
band design, it may be necessary to increase the electrode
dimensions at wider bandwidths, Therefore, wider bandwidth
filters can be expected to have more and stronger spurious
responses. However, one can always take advantage of narrow
band design by operating the crystal filter at a higher frequency
with the reduced percentage bandwidth, such that the spurious
response will be improved for a given bandwidth requirements.
Group Delay Distortion
Group delay, also called envelope delay, is the time taken for a
narrow-band signal to pass from the input to the output of a
device. Group delay distortion is the difference between the
maximum and the minimum group delay within a specified pass
band region or at two specific frequencies. For most bandpass
filters, the delay response will have a peak close to each
passband edge, where the filter attenuation begins to increase
rapidly. Filer delay and attenuation characteristics are
interdependent. The more rapidly the filter attenuates, the larger
the delay peaks. In general, large delay peaks are associated
with filters having many poles or filters that have close-in
stopband poles (such as elliptic function filters). On the other
hand, the MCFs have a very small group delay distortion,
typically less then 10 μs.
Inter-modulation (IM)
Inter-modulation occurs when a filter acts in a nonlinear
manner causing incident signals to mix. The new frequencies
that result from this mixing are called inter-modulation products,
and they are normally third-order products, which means that a
one dB increase in the incident signal levels produces a 3 dB
increase in IM. The IM can be classified in the following two
types:
Out-of-bend inter-modulation occurs when two incident signals
(typically -20 to -30 dBm) in the filter stopband produce an IM
product in the filter passband. This phenomenon is most
prevalent in receiver applications when signals are present
simultaneously in the first and second adjacent
channels. This IM performance of crystal filters at low signal
levels is primarily determined by surface defects associated with
resonator manufacturing process and is not subject to analytical
prediction.
In-band inter-modulation occurs when two closely spaced
signals within the filter passband produce
IM products that are also within the filter passband. It is most
prevalent in transmit applications
where signal levels are high (typically -10 dBm and +10 dBm).
This IM performance at high signal
levels is a function of both the resonator manufacturing process
and the nonlinear elastic properties
of quartz. The latter is dominant at higher signal levels, and can
be analyzed.
IP3
Third Order Input Intercept Point: The point at which the power in
the third-order product and the fundamental tone intersect, when
the amplifier is assumed to be linear. IIP3 is a very useful
parameter to predict low-level intermodulation effects.
Phase shift/Minimum Phase Transfer Function
The change in phase of a signal as it passes through a filter. A
delay in time of the signal is referred to as phase lag and in
normal networks, phase lag increases with frequency, producing
a positive envelope delay.
The great majority of crystal filters are minimum phase shift
filters. Mathematically, this means that there is a functional
relationship between the attenuation characteristic and the
phase characteristic of the filter. The transfer function of such a
two-port network is said to have the minimum phase shift
property, which means that its total phase shift from zero to
infinite frequency is the minimum physically possible for the
number of poles that it possesses.
Terminating Impedance
This is the required impedance to be seen on input and load side
of the filter to maintain a good characteristics response.
Terminating impedance is typically
specified as a series resistance with a parallel capacitance that
should also include the stray capacitance of the circuit board.
Power Handling
Power handling is usually specified as the maximum input
power. In design, it is closely related to the factors determining
in-band inter-modulation performance. Given the bandwidth,
insertion loss and spurious response requirements, the
power handling capability of a filter can be estimated.
Vibration-induced Sidebands
Vibration-included sidebands may appear on a crystal filter
output signal when the filter is subjected to mechanical vibration.
Vibration produces acceleration forced on the crystal resonators,
causing their resonance frequencies to change slightly –
typically a few parts per billion for one G acceleration. For
Sinusoidal vibration, the resonance frequency is modulated at
the frequency of vibration, and the peak deviation is determined
by the acceleration sensitivity of the crystal resonator and the
amplitude of vibration.
Viewed on a spectrum analyzer, the filter output will have
sidebands offset from the carrier by the frequency of vibration.
For most filters, the vibration-induced sidebands are quite small
and of no concern. However, narrowband spectrum cleanup
filters may require special attention. Vibration-induced sidebands
are minimized by minimizing resonator acceleration sensitivity
and by control of mechanical resonance within the filter structure.
Settling Time and Rise Time
Settling time is the time it takes for the output signal to settle
within a specified overshoot percentage after the input has been
subjected to a step response, pulse, impulse, or ramp rise time is
often defined as the time required for the output of a filter to
move from 10% to 90% of its steady state value on the initial
rise. While the exact value of rise time can readily be calculated
or determined form filter handbooks, the following rule
of thumb relating rise time to bandwidth provides an useful
estimates.
Tr – 0.35/fc
Where Tr is the rise time in seconds and fc is the 3 dB cut off
frequency in hertz
Discrete Crystal Filter
Bandpass RF filter utilizing high Q Quartz resonators and LC
Components. Provides highly selective frequency rejection as
well as very flat passband response.
Typical Half Lattice
Parasitic capacitances of each crystal cancel each other out to
allow the circuit to operate. Adopting different crystal
Frequencies allows for very wide bandwidths.
Discrete Filter Types
Narrowband
Intermediate
Wideband
Typical Characteristics
Standard Frequencies
1 MHz,
10.7 MHz
1.8 MHz
21.4 MHz
2.62 MHz
45.0 MHz
5.0 MHz
70.0 MHz Fundamental/3rd Overtone
70.0 MHz to 250.0 MHz Fundamental Inverted Mesa Technology
Shape Factor
60 to 3 dB
4 pole = 4:1 Ratio
6 pole = 2.5:1 Ratio
8 pole = 2.0:1 Ratio
10 pole = 1.6:1 Ratio
12 pole = 1.35:1 Ratio
Example: 60 dB B.W = 60 KHz Max
3 dB B.W = 30 KHz Min
60 dB/3 dB = 2:1 Ratio = 8 pole filter
Bandwidth
Ratio = B.W / Center Frequency
Narrowband
Ratio = Narrowband Design B.W = .32% or less of Center
Frequency
Intermediate
Ratio = Intermediate Design B.W = .3% to 1% of Center
Frequency
Wideband
Ratio = Wideband Design B.W = 1% to 10% of Center
Frequency
Typical Filter Response
4 Pole Half Lattice Intermediate Response
Filter Data Sheet
The following data sheets provide a comprehensive look at many
of our most popular filters. Please keep in mind that in parallel to
this offering, we manufacture custom filters as well!
Monolithic Crystal Filter
Traditional Crystal filters use several discrete crystal and
external components. Monolithic Crystal filter uses a single
crystal element and two sets of electrodes are placed in the
mechanical resonances in the crystal to give highly selective
filter.
Monolithic Equivalent Circuit
The Operation of the filter can be explained in terms of
its equivalent circuit. L3 represents the internal coupling between
the two resonant circuits whereas Co and Cp are the parasitic
capacitances in the circuit, Co is the capacitance between the
top and bottom plates at either end of the quartz element. Cp is
the parasitic leakage capacitance across the resonant element.
Typical Frequency Range
Standard If Frequencies
5 MHz to 45 MHz
45 MHz to 90 MHz 3rd Overtone
DSP Roofing Filters
60 MHz to 250 MHz fundamental
Inverted Mesa Technology
Shape Factors
60 to 3 dB
4 pole = 4:1 Ratio
6 pole = 2.5:1 Ratio
8 pole = 2.0:1 Ratio
10 pole = 1.6:1 Ratio
12 pole = 1.35:1 Ratio
Example: 60 dB B.W = 60 KHz Max
3 dB B.W = 30 KHz Min
60 dB/3 dB = 2:1 Ratio = 8 pole filter
Bandwidth Fundamental
5 MHz 1 KHz – 10 KHz
10.7 MHz 1 KHz -30 KHz
21.4 MHz 1 KHz -50 KHz
30.0 MHz 1 KHz -50 KHz
45.0 MHz 1 KHz -50 KHz
70.0 MHz 10 KHz -120 KHz
Inverted Mesa 90.0 MHz 10 KHz -120 KHz
Inverted Mesa 110.0 MHz 10 KHz -150 KHz
Inverted Mesa 150.0 MHz 10 KHz -150 KHz
Inverted Mesa 200.0 MHz 10 KHz -150 KHz
Inverted Mesa 250.0 MHz 10 KHz -150 KHz
3rd Overtone
70 MHz 1 KHz -25 KHz
90 MHz 1 KHz -25 KHz
100 MHz 1 KHz -25 KHz
140 MHz 1 KHz -25 KHz
Typical Monolithic Schematic
Typical Filter Response
Typical Filter Response
Standard 3rd overtone 2 pole
Typical Filter Response
Standard 5x7 Inverted Mesa 2 pole
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