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Electronics II Tutorials
   Overview Analog Wireless Communcation
   Resistors, Capacitors, RC Networks
   Diodes, Amplitute Modulation, Diode Detection
   RL Circuits, Inductive Kicks, Diode Snubbers
   RC filters. Series resonance and quality factor, Matching, Soldering
   Ladder filters Butterworth and Chebyshev filters Filter tables ADS
   Bandpass ladder filters Quartz crystals
   Impedance inverter
   Ideal Transformers
   Transformer shunt inductance
   BJT-Large signal models
   Transistor switches. Voltage regulators
   Transistor switches. Voltage regulators
   Common emitter amplifier. Max. efficiency of class A amps. Transformer coupled loads
   Available power. Distortion. Emitter degeneration. Miller effect
   Emitter follower and differential amplifiers
   JFET Source follower amplifier
   Oscillators. Clapp oscillator. VFO startup
   Variable frequency oscillator. Gain limiting
   Receiver incremental tuning. Crystal oscillators
   Mixers. Gilbert cell
   Superheterodyne receivers. Spurious responses of mixers
   Decreasing channel bandwidth by using CW
   Audio amplifiers
   JFETs as variable resistors
   Automatic gain control
   Noise, SNR, MDS, noise power density and NEP
   Nyquist noise formula. Cascading noisy components. Noise figure
   Receiver intermodulation and dynamic range
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Bandpass Ladder Filters Quartz Crystals

Bandpass Ladder Filters. Quartz Crystals
In addition to low- and high-pass filters, ladder filters can also be used to construct higher-order bandpass and bandstop (i.e., notch) filters. Circuit diagrams for a four element (i.e., second order) bandpass and bandstop filters are shown below.

For bandstop filters, simply interchange the two sections

These filters can be synthesized using the same filter tables we used for low- and high-pass ladder filters. However, there are some important differences. Here is the procedure for a bandpass filter:
1. The filter tables are used to compute the series inductances and shunt capacitances as we did with the low-pass filter.
2. When un-normalizing, use the 3-dB bandwidth ?? rather than ?c to find the Ls and Cs.
3. Finally, compute the series Cs and parallel Ls using the resonant frequency condition ?0 =1 under root LC . We will now consider the same example shown in the text on pp. 104-105. (In Prob. 8 you will build and test the series LC network portion of the RF Filter.)
Example Here we will design a second order Butterworth bandpass filter (Fig. 5.7a) using L1 and C1 as one section. We require that f0 = 7 MHz and R = 50 ?. With L1 and C1 specified, we have one half of the filter already: We will now consider the same example shown in the text on pp. 104-105. (In Prob. 8 you will build and test the series LC network portion of the RF Filter.)

Now, from Table 5.1, a1 =under root 2 . Recall that

Consequently, ?? = a1 R /1510?6red or ?f = ??/2?= 750 kHz. This ?f is the 3-dB bandwidth of the filter. (At 7 MHz, this ?f is somewhat large, meaning this is a relatively low- Q filter.) Next, using the filter table again, we will determine the shunt C2 From

The complete filter design is shown below

While this example was seemingly just an exercise, believe it or not, the actual RF Filter in the NorCal 40A is a two-element Butterworth bandpass filter! L1 and C1 are the series L and C, but where is the parallel L and C?
This second section is provided by the primary winding of T2 (? 66 nH). The transformer also transforms the impedance of C2 to the primary side (youll see this later in Lecture 15). Consequently, 20 p C ?? nF or so. Thats just whats needed for this second order Butterworth bandpass filter! Youll see more with this aspect of the RF Filter in Prob. 16 when you construct and install T2.
Quartz Crystals
The maximum Q (minimum bandwidth) of LC ladder filters is usually limited by the inductor Q (i.e., the inductor losses). Other types of resonant elements must be used if Qs higher than a few hundred are desired. Such Qs are useful from audio to microwave frequencies.
Quartz crystals are one such element. These are made from silicon dioxide, which is cheap. The Qs of such quartz crystal resonators range from 25,000 to 150,000! Another advantage is that a small temperature coefficient can be obtained for quartz crystals. This is useful so that the resonant frequency drift with temperature is minimized as the transceiver warms up, or in other situations. Quartz crystals make good electrical resonators because of the
piezoelectric effect. This effect is a combination of a mechanical vibration and bound electric charges. When a quartz crystal is squeezed, a voltage is produced:

Electric starters for gas furnaces, water heaters and grills use such a piezoelectric effect. This piezoelectric effect also works the other way. A voltage applied across a quartz crystal causes a small expansion of the crystal

A microscopic view of the atoms in the quartz lattice helps us understand this piezoelectric effect

These quartz crystals can be modeled as RLC filters in electrical circuits:

The equivalent electrical circuit for the quartz crystal is

You will operate your quartz crystals in series resonance in the NorCal 40A. Why is there variation with frequency? Because the mechanical vibrations of the lattice will not be as favorable for llfrequencies of voltage excitation. At some frequencies, the lattice vibrations are maximum.

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