# Interconnection and Timing of Digital Circuits Tutorial (page 2)

 Page 1 At this page (2) ⚛ Interconnection of Digital Circuits ⚛ Timing of digital circuits ⚛ Basic Principles of Interconnection ⚛ Timing circuits with logic gates ⚛ Interconnection of Different Logic families ⚛ Crystal oscillators ⚛ Interfacing TTL and CMOS circuits ⚛ Integrated oscillators ⚛ Switching Low Voltage CMOS Circuits ⚛ Interconnection of TTL / CMOS and ECL Circuits ⚛ Open Collector Output Connections

## Timing of digital circuits

The operation of digital circuits is clocked with one or more clocks. These signals are crucial for the proper operation of digital systems, especially in the case of high frequency operating circuits. The following paragraphs show various forms of timing, low and high precision circuits.

## 4.2.1 Timing circuits with logic gates.

By combining logic gates, R and C components, it is possible to synthesize timing circuits for systems that do not require large operating frequencies and high timing accuracy.

Figure 4-3

The circuit of Figure 4-3 is a monostable multivibrator (one-shot): the circuit is in a steady state, and for a short time it can be in an unstable state before returning to its original equilibrium state. The circuit consists of two CMOS gates (NOR and inverter) and the elements R and C. The circuit operation is as follows:

In time t = 0 the input voltage VP = 0, the voltage V2 = VCC and the output voltage Vo = 0. Therefore the voltage V1 at the output of the NOR gate is high and the circuit is in equilibrium mode.

In time ti the VP input goes into high state for a short time. V1 switches to low state and momentarily the same happens with V2, because capacitor C keeps the voltage previously existing on its terminals (0V). Thus Vo output goes to high (HIGH).

But then, C is exponentially charged by resistance R and V2 approaches the inverter's VT threshold voltage in time:

T = RC·ln(VCC/(VCC - VT))

At that moment, Vo becomes '0' and, since VP has already returned to a low state, V1 becomes HIGH. As capacitor C is charged at VT voltage, V2 momentarily follows the change by overcoming the VCC until the D protectors at the input of the inverter begin to convert to VCC + VD voltage. V2 then returns exponentially to the VCC value.

The accuracy of the pulses produced by the circuit of Figure 4-3 is not high, because it depends on the values ​​of VT, R and C, which have variations and tolerances for each component. The activation pulse at the VP should be greater than the propagation delay of the two gates so that '1' can return to the NOR input for pulse maintenance.

Figure 4-4

Figure 4-4 illustrates a circuit with two CMOS inverters, the output of which continuously switches over at fixed intervals from one logic state to the other. This circuit is called "astable multivibrator" or oscillator.

Assume that at time t = 0, the V1 exceeds the threshold voltage VT of the first inverter. Then V2 becomes '0' and Vo output is '1' (VCC). Through capacitor C, this change returns to V1, which obtains instantaneous the value of VCC + VT.

Then C is discharged via R to V2 (which is '0') and voltage V1 drops. When V1 becomes less than VT, V2 becomes '1' and Vo output goes low. The output change affects V1, which is instantly decreasing by VCC and acquires the VT-VCC value. The return time of V1 at the threshold voltage is equal to:

T1 = RC·ln((VCC+VT) / VT)

Then, C is charged by R from V2 (now it is in high state) and voltage V1 is increasing. When V1 reaches the VT again, V2 becomes '0' again and Vo becomes '1'. The circuit continuously repeats the oscillation. The time required to reach V1 the threshold voltage is:

T2 = RC·ln( V- 2VCC / VT - VCC )

In circuit analysis of Figure 4-4, the influence of input protection diodes of the first inverter must also be taken into account: in fact V1 ranges between VCC + VD and VD.

The two times T1 and T2 are equal when the threshold voltage equals VCC / 2. In each case, the period of the generated clock signal is equal to the sum of these two times.

## 4.2.2 Crystal oscillators.

The circuit of the previous paragraph can produce simple low-precision clock and 1MHz clock waveforms. Higher-frequency clock signals are produced using crystal oscillators.

Before analyzing the circuit of a crystal oscillator, some theoretical elements for the operation of an oscillator and the physical properties of the quartz crystals are listed below.

Figure 4-5

An oscillator consists in its theoretical form of an amplifier circuit and a filter, which are connected to a positive feedback loop (Figure 4-5). To operate the circuit as an oscillator,

• a) the gain in the loop must be greater than one.
•
• b) the total phase shift of the signal to be multiples of 2π.

In Figure 4-5 the amplifier reverses the signal by shifting the phase by 180o while the filter still adds 180o for a total phase shift of 360o. The amplifier also provides the required gain (>1) to amplify the signal to a steady state, Where the gain is 1.

The filter determines the operating frequency of the oscillator and provides a coupling between the output and the input of the amplifier. Discrete elements L and C can be used to implement the filter, but a quartz crystal is usually used for this purpose.

Quartz is piezoelectric. This means that when an electric field is applied to it, a physical shift (oscillation) of the material occurs, and vice versa. The quartz crystals are processed into thin sections and have a very stable primary oscillation frequency depending on their cutting. It is possible to make crystals with oscillation frequency up to 40MHz, while frequencies up to 300MHz use higher harmonic oscillations.

A quartz crystal is described by the equivalent circuit of Figure 4-6 and oscillates at two major frequencies:

• A) At the co-ordination frequency in series, C1 and L1 are tuned in such a way that the crystal resembles a small resistor R1.
•
• B) At the parallel resonance frequency, the combination of L1 and C1 is inductive and coordinated with Co.
•

Figure 4-6

The two frequencies differ by about 0.1%. The crystals are constructed to operate in one of two modes of tuning. Constructively, there is no difference between the two types, just the nominal oscillation frequency of the crystal differs. In addition, for the parallel tuning, the required external load CL is determined for oscillation exactly at the indicated frequency.

In the circuit of Figure 4-7 with a CMOS inverter, the circuit operates in parallel resonance. Thus it behaves as an inductive element and together with the capacitors C1 and C2 it shifts the signal by 180o. C1 and C2 represent the capacitive load of the crystal and usually have a similar value.

Figure 4-7

Resistor R1 holds the inverter in the active operating range (between '0' and '1'), while R2 isolates the inverter output from the crystal network, allowing a cleaner output waveform to be produced.

The CMOS inverter provides the first 180o phase shift of the signal phase in the feedback loop and at the same time amplifies the signal (the gain of such an inverter in the active region is greater than 10). The circuit begins to oscillate with the influence of the ambient electrical noise and the signal is successively amplified until the oscillator enters a steady state. In this final state, the oscillation is self-sustaining at a frequency equal to the frequency of parallel crystal tuning.

## 4.2.3 Integrated oscillators.

In modern high-frequency digital circuits, integrated crystalline oscillator circuits are used in sealed metal packages instead of discrete circuitry such as the one in the previous paragraph. The accuracy of integrated oscillators is crucial for the required timing of digital systems and must be carefully selected based on their functional characteristics.

The main parameters that characterize an integrated oscillator are:

• • The rated operating frequency (MHz)
•
• • Operating mode (tuning type)
•
• • Stability of oscillation (percentage of divergence)
•
• • Frequency shift with "aging" (deviation per year)
•
• • Operating conditions (temperature, power, load, etc.)
•
• • The type of signal produced (TTL, CMOS or ECL levels)