Monolithic Crystal Filters 2 Quartz resonator internally coupled utilizing piezoelectric effect.

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1 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

2 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.

3 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

4 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

5 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.

6 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

7 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

8 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.

9 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.

10 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.

11 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

12 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 MHz Fundamental Inverted Mesa Technology

13 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

14 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!

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17 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.

18 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 MHz 10 KHz -150 KHz Inverted Mesa MHz 10 KHz -150 KHz Inverted Mesa MHz 10 KHz -150 KHz Inverted Mesa 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

19 Typical Monolithic Schematic Typical Filter Response

20 Typical Filter Response Standard 3rd overtone 2 pole Typical Filter Response Standard 5x7 Inverted Mesa 2 pole Thank you! Please call us at (800) with any questions you may have.