Design and Synthesis of a MOD 13 Binary Down Counter

This work explains the process of designing and synthesizing a MOD 13 binary down counter using 180 nm CMOS technology transistors. The beginning of the count is a combination of 1110 2 , the end of the count is 0010 2 . Simulations are made at the circuit level (transient analysis) to verify that the circuit functions correctly, then the integrated circuit layout is prepared by connecting the components manually. Finally, the layout is simulated to see how the existence of parasitic resistances and capacitances affect the output signals and it is used to estimate the maximum allowable clock frequency (f clk ).


General overview
A digital counter is an electronic device that counts how many times a specific event occurred [1][2][3][4][5][6][7][8]. Digital counters are usually driven by a clock. The most widely used scheme is a sequential circuit consisting of flip flops and a clock signal, counters can be implemented using different types of flip flops. The outputs represent the bits for example, for a MOD-16 counter, we need 4 flip flops in a cascade, they either count up or down. Counters are widely used in different industries for different applications.
Design and Synthesis of a MOD 13 Binary Down Counter

Types of digital counters
Digital counters have different kinds, each is suitable for a certain application, they can be broadly classified into two groups: synchronous counters and asynchronous (ripple) counters.
In synchronous counters, as the name indicates the flip flops share the same clock, meaning the output of each flip flop is connected to the input of the next element, an example is shown below: In contrast, asynchronous (ripple) counters work without a synchronous clock, the output of the previous flip-flop is given to the input of the following flip-flop as a clock signal which are connected in series, and the clock pulse laps through the counter. Because of the ripple clock pulse, it's also known as "ripple counter". Asynchronous (ripple) counters are able to generate 2 n -1 unique binary combinations.
The two types described above are very broad categories, they can be manipulated to design tens of other counters, other classified groups include: Modulus counters, up/down counters, ring counters, Johnson counters, decade counters, binary coded decimal counters, gray-code counters.

Applications
Counters are generally used in counting applications. They measure the time interval between two instants of time or frequency of a certain signal. Many common devices like processors, calculators, clocks, ovens use some kind of digital counter. They are also used in alarms, air conditioners, car parking controllers and so on.
In addition to that, they can be used as a clock divider circuit. Modern counters usually have different features, for example presetting the counter for determining the initial step. In certain cases, they are used in machinery controls. In electronics world, counters got wide usage in multiplexer circuits, digital clocks, staircase voltage generators and analog/digital converters.

The truth table
The truth table can be obtained from the counter requirement (starting at 14 and ending at 2), as shown below:

Karnaugh-maps and output expressions
The flip-flop output expressions can be obtained using Karnaugh-maps, as following:

Implementation on circuit level
The block diagram of the MOD 13 counter is provided in fig. 2

Results
After running the simulation (LVS) the following output signals were obtained:

Layout design
In section 2.6, the layouts are prepared for the previously proposed circuits. Layout is created for each element separately, then they are connected through metals.

Summary
The transistor sizes used in the designs are provided below:

Conclusion
The design of the MOD-13 down counter was successfully implemented using UMC_CMOS 180nm technology in Cadence Virtuoso, the counter starts counting at 14 (1110 2 ) and ends at 2 (0010 2 ). The maximum operating frequency is 1.4 GHz, using clock frequency higher than this value isn't allowed because the triggers start to work improperly, and the output signals will get distorted.