Design scheme for generating accurate clock source from oscillator

Digital logic has become the core of all electronic circuits today, whether it is FPGA, microcontroller, microprocessor or discrete logic. Digital systems use many components that must be interconnected to perform the required functions. The essential element to ensure the proper operation of such digital systems is the clock signal that enables communication and synchronization between all digital components. Therefore, we always need a source to generate this clock signal.

The signal source is in the form of an oscillator. Although most microcontrollers today have an integrated RC oscillator, the quality of the clock generated by this internal RC oscillator is often not sufficient to support the accuracy required to communicate with other modules in the system. Therefore, an external oscillator is required that can provide a clock signal for the entire system and meet all requirements for accuracy, signal integrity and stability.

This article focuses on the different aspects of oscillators that generate accurate clocks over temperature and time. Topics covered include:

Oscillator - Basic standard of oscillation

● Quartz crystal oscillator

● Q factor and its importance

● Different types of crystal oscillators

The remainder of this article will cover the design and provide detailed instructions on:

● Pierce Crystal Oscillator (XO)

● Voltage Controlled Oscillator (VCXO)

● Temperature Controlled Oscillator (TCXO)

● Oven-controlled oscillator (OCXO)

● Importance of negative resistance

What is an Oscillator?

In electronics, any circuit that generates a repetitive signal without the need for an input can be called an oscillator. In simple terms, an oscillator converts DC energy into AC energy of a desired frequency. The frequency of oscillation is determined by the constants of the components used in the design of the oscillator. Oscillator circuits generally use amplifiers with positive feedback; in order to maintain oscillation, the circuit must adhere to the Barkhausen criterion; that is, the gain of the closed-loop oscillating system must be an integer, and the phase shift around the loop must be 2nπ, where 'n' can be any integer, as shown in Figure 1.

Figure 1: Closed-loop oscillator system

At the initial excitation, the only signal in the circuit is noise. Due to the positive feedback mechanism, the noise component that meets the oscillation frequency and phase conditions will propagate through the system and increase in amplitude. The signal amplitude continues to increase until it is limited by the internal characteristics of the active components themselves or by an external automatic gain control (AGC) unit. The time required to establish oscillation depends on many factors, such as the amplitude of the noise signal and the gain of the loop.

There are various oscillators that can be used to establish oscillation, such as: RC oscillators, LC oscillators and quartz oscillators. However, in terms of precision and accuracy over a certain temperature and time range, quartz oscillators are preferred because they have high Q (in the range of 104 ~106, compared to 102 for LC, as described later), which helps to achieve higher stability over temperature and time.

Quartz Oscillator

The biggest selling point of quartz crystal oscillators is their ability to generate a constant frequency under a wide range of load and temperature conditions. In a quartz crystal oscillator, when a voltage source is applied to the crystal, it produces a mechanical perturbation that generates a voltage signal at a specific frequency (also known as the resonant frequency). The frequency generated depends on the shape and size of the crystal, so after the crystal is cut, it cannot be used for any other frequency. The thinner the crystal, the higher the resonant frequency.

The equivalent circuit of the crystal oscillator is:

A quartz crystal can be modeled as an LCR circuit as shown in Figure 2.

Figure 2: Equivalent circuit of a crystal oscillator

Where Lm, Cm and Rm are the motional inductance, motional capacitance and motional resistance of the crystal, respectively, and Cs is the shunt capacitance formed by the electrical connection of the crystal. The quartz oscillator operates at two resonant frequencies: the series resonance frequency (fs) formed by the series resonance of Ls and Cs, and the parallel resonance frequency (fp) formed by the parallel resonance of Ls and the series combination of Cs and Cp. The parallel resonance frequency is also called the operating base frequency.

Figure 3: Resonator reactance vs. frequency

Figure 3 illustrates the reactance vs. frequency curve of a crystal. At frequencies far from fp, the crystal behaves capacitively. In the region between fs and fp, it behaves inductively. The region between fs and fp is the normal operating range of the crystal. Oscillator and Stability:

For oscillators, there are many factors that affect the frequency stability of the system, such as: aging, noise, temperature, holding circuit, retentivity, magnetic fields, humidity, power supply voltage and vibration. Here are some important factors:

Instability caused by time

Instabilities due to time can be divided into two categories - aging and short-term instabilities. Aging is a long-term systematic change in frequency due to internal variations in the oscillator. However, although this frequency variation is only a few PPM, it is critical when it comes to systems that require precise frequencies (such as: DTV, set-top boxes, etc.). In contrast, short-term instabilities are essentially random in nature and can often be defined as noise.

Aging - Aging is caused by many factors such as mass transfer, stress on the crystal, thermal expansion, mounting forces, bonding units, drive levels to the crystal, and DC bias.

Short-term noise - The output of an ideal oscillator is a perfect sine wave. However, in an ideal system, random noise or flicker noise can cause the phase of the signal to shift, causing the frequency to change in order to maintain the 2nπ phase condition. The phase slope dφ/df is proportional to QL and must be kept high to ensure the highest frequency stability. In order to maintain a high phase slope, Cm should be as small as possible. Therefore, the larger the slope of reactance/frequency between fs and fp, the higher the frequency stability.

Instability caused by temperature

The resonant frequency of a crystal oscillator changes very little at room temperature. However, as the temperature rises to extremes, the variation in the rated frequency begins to increase, potentially reaching tens of ppm.

Applications such as computing can tolerate this. However, for applications such as navigation, radar, radio communications, satellite communications, etc., which require extremely high accuracy and precision, such large changes are unacceptable. Therefore, such applications require additional compensation components to be added to the system (see below).

Tunability Causes Instability

Making the oscillator tunable over a wide frequency range can lead to instability. To achieve tunability, filters are needed to eliminate unwanted frequency modes. However, this makes it difficult to achieve higher frequency stability with a tunable oscillator because the load reactance is affected by the stray capacitance and inductance of the varactors used in the filter.

Keep the circuit from being unstable

When adding external load capacitors to a crystal, the tolerance of the capacitors and stray capacitance can cause the actual load capacitance to deviate from the desired value. This change in load capacitance will also cause a change in frequency. This can be found from the following equation:

in,

Cm is the crystal oscillator capacitance specified in the crystal data sheet;

CS is the crystal shunt capacitance specified in the crystal data sheet;

CL_NOM is the load capacitance specified in the crystal datasheet;

CL is the actual capacitance between the crystal terminals.

Q Factor

The Q factor determines the ratio of the energy stored in the resonator (the energy stored in L and C) to the energy lost (the energy dissipated in R). Some of the advantages of using a higher Q factor are:

● Using a higher Q factor can reduce phase noise, because phase noise has a strong dependence on the Q factor of the crystal. This can improve frequency stability.

● Another advantage of higher Q factor is reduced bandwidth.

● The Q factor is proportional to the time from excitation to decay. Therefore, the higher the Q factor, the longer the decay time. The decay time and loop gain together help to shorten the start-up time of the crystal oscillator.

Types of Crystal Oscillators

Crystal oscillators can be divided into four categories based on the compensation method used to achieve higher precision and accuracy. The most commonly used crystal oscillators include:

● Uncompensated Crystal Oscillator - XO

● Voltage Controlled Crystal Oscillator - VCXO

● Temperature Controlled Crystal Oscillator - TCXO

● Oven Oscillator - OCXO

Compensated Crystal Oscillator (XO)

As mentioned previously, such oscillators can vary greatly over temperature - on the order of ±15ppm. For applications that do not require a very precise clock, an uncompensated crystal oscillator is a good choice.

Voltage Controlled Crystal Oscillator (VCXO)

Voltage controlled crystal oscillators use a very basic property of the crystal - that it will resonate at a specified frequency only if the load capacitance (CL) at the oscillator terminals matches a certain value usually called CL_NOM (usually provided by the crystal manufacturer). For example, if the crystal is specified as 25Mhz with 14pF, it means that it will resonate at 25MHz with 0PPM error only if the CL provided at the oscillator terminals is 14pF. From Equation 1, it can be seen that increasing CL can reduce the PPM error in frequency. If CL > CL_NOM, then the ppm becomes -ve, which means that the crystal will resonate at a frequency lower than the center frequency. While CL

This property of crystal oscillators is realized in VCXOs, which need to track the frequency accurately within a very small range, such as for digital set-top boxes, DTVs, etc. VCXOs use an additional varactor diode connected to its input terminals (or any other means of changing the CL at the oscillator terminals, such as: sometimes a digitally controlled capacitor array is used). This diode is connected in reverse bias mode and an external voltage is applied across it. Due to the characteristics of the varactor diode, its capacitance changes with the applied voltage (i.e., it decreases with increasing reverse bias voltage), and the same is true for the CL at the oscillator input. Therefore, we can control the frequency of oscillation and fine-tune the circuit by changing the voltage across the diode. In practical applications, an error voltage can be generated by comparing the output frequency with the expected frequency.

Temperature Controlled Oscillator (TCXO)

The TCXO works on the same principle as a VCXO - when a reactive component (capacitor or inductor) is connected in series with the crystal, the frequency of oscillation can be changed (see Figure 3 - the area between fs and fp). The TCXO uses a temperature sensor to measure the temperature and provide a correction signal to the varactor diode to compensate for the change in frequency.

Figure 4: TCXO block diagram

The block diagram of a TCXO is shown in Figure 4. Using this method, an accuracy of 0.1ppm can be achieved.

Constant temperature oscillator

In this configuration, the crystal and other temperature-sensitive components are placed in a temperature-controlled chamber (oven) that is adjusted to a temperature at which the frequency/temperature slope of the crystal is 0. This allows the oscillator to achieve the highest stability with respect to temperature, in the order of 0.001ppm.