Microelectronic Filters

ABSTRACT

Considering oscillator circuits are implemented in almost every electronic product today, these fundamental circuits can be thought of as the foundation for many devices. Oscillator circuits provide clean and dependable signals to drive other devices, so as to provide a reference or clock signal in the form of a square wave, triangle wave, or sine wave. For example, oscillators are used to operate key functionality in metal detectors, radios, and stun guns.

In order to design a collector-coupled BJT oscillator, also known as a relaxation oscillator, a sufficient amount of calculation and simulation time is required. Using PSpice to simulate the collector-coupled BJT oscillator, transient analysis and frequency response curves can be used to determine key signal parameters, such as amplitude, frequency, total harmonic distortion (THD), and DC offset voltage. After simulation, practical implementation can be used to attain these same parameters to determine the percentage error due to factors not accounted for during simulation. For example, affects due to inaccurate component values and attenuation in signal strength from power loss definitely contribute to attaining a nonzero percentage error. However, if time is taken into designing the collector-coupled BJT oscillator, factors such as inaccurate component values can be minimized, and a more ideal output waveform can be generated.

INTRODUCTION

1. Background

An electronic oscillator is a device that produces a periodic signal, such as a square wave, a triangle wave, or a sine wave, so as to provide a clock source or reference signal for another device. Two basic types of oscillators include linear and nonlinear types, where linear oscillators use feedback to manifest a desired output signal, and nonlinear oscillators use transistors and capacitors to interchange nonlinear states to achieve a certain output. Also, even though oscillator designs can vary in a myriad of ways, one common design parameter shared by all oscillators is the fact that they do not have an input signal.

Oscillator circuits are key components to the majority of electronic devices because they provide the foundation for allowing electronic equipment to function properly. For example, in order for a computer to function correctly, its microcontroller must sink the output of a crystal oscillator so operation codes and interrupts can be executed in a proper cycle. In general, oscillator circuits are implemented in a variety of electronic equipment, such as function generators, wireless receivers and transmitters, and music synthesizers.

The actual implementation of an oscillator can be very difficult, as inaccurate component values can degrade the precision of a desired output. However, with proper design calculations and effective component implementation, a specific output can be realized. Using an explicit set of equations, the circuit in Figure 1 below, was simulated in PSpice and then implemented on a breadboard, so as to achieve the following design specifications:

• Output пÑ" Sine wave

o Frequency of oscillation (f0) пÑ" 4.07 kHz

o Vpk-pk = 4 V, DC level = 0 V

o Total Harmonic Distortion (THD) ≤ 5%

In completing this design, the main objective was to attain a sine wave at the Vout node so an error percentage, with respect to the above-stated design specifications, of less than or equal to 5% could be achieved.

2. Theory

In analyzing the nonlinear nature of the collector-coupled BJT oscillator in Figure 1, it can be seen that the two NPN BJTs are used as switches in the circuit, where one transistor is operating in saturation, the other transistor is operating in cutoff. The on-off behavior of these BJT devices allows the capacitor connected to the transistor in saturation to charge through resistor R7 or R8, until the base voltage of that transistor reaches cutoff. This process continues without end until the collector-coupled BJT oscillator is forced into a state of stability. Now, considering this oscillator circuit produced a square wave at the collector nodes of transistors Q1 and Q2, it was determined that a Sallen-Key bandpass filter with a center frequency set at the oscillator’s fundamental frequency would be required to generate a sine wave. The function of the bandpass filter in Figure 1, was to transform the square wave to a sine wave by filtering out all the harmonic frequencies, so a sine wave with a frequency of 4.07 kHz could be produced at Vout.

3. Calculations and Simulations

The values for the capacitors and resistors in Figure 1 had to be calculated and validated using PSpice, MathCAD, and Eq. 1 below.

f0 = Eq. 1

Using Eq. 1, the values for resistors R7 and R8, where R7 = R8, were calculated after capacitors C3 and C4, where C3 = C4, were set to a capacitance value of .015uF. Once these values were obtained, the collector-coupled BJT oscillator was simulated in PSpice. The reason for choosing .015 uF as the value for C3 and C4 was due to constraints with the availability of capacitors in the ECE 3042 lab. Therefore, in order to design an oscillator with an error percentage less than or equal to 5%, it was necessary to implement the most accurate component values based on what was actually in stock. It should also be noted that choosing a different capacitor value should not have an effect on the complexion of the output signal, as the center frequency is set to a constant value.

Once the appropriate square wave was obtained at the output of the collector-coupled BJT oscillator, a bandpass filter with a center frequency of f0 = 4.07 kHz needed to be designed. Using MathCAD, the values for the resistances and capacitors in the Sallen-Key bandpass filter were obtained, where the quality factor Q, was set to a value of 20 and the center frequency was set to a value of 4.07 kHz. Using Eq. 2,

Q = Eq. 2

where в?†f is the bandwidth, it was determined that setting Q equal to 20 would allow for an insignificant bandwidth of 203.5 Hz. This means that the Sallen-Key bandpass filter would allow frequencies in the range of 3.8665 kHz - 4.2735 kHz to pass through to the output. In Figure 2(a), the transient response of the bandpass filter output is shown, and in Figure 2(b), the frequency response of the bandpass filter output is