This repository presents the design of Frequency Divider Using Astable Multivibrator and MOD-4 Counter as a mixed signal circuit. The Astable Multivibrator is designed as an analog circuit while the MOD-4 Counter is designed as a digital circuit.

• Abstract
• Reference Circuit Diagram
• Reference Waveform
• Circuit Details
  • Astable Multivibrator
  • MOD-4 Counter
• Software Used
  • eSim
  • NgSpice
  • Makerchip
  • Verilator
• Circuit Diagram in eSim
• Verilog Code
• Makerchip Code
• Makerchip Plots
• Netlist
• NgSpice Plots
• Observations
• Steps to run generate NgVeri Model
• Steps to run this project
• Acknowlegdements
• References

Frequency Divider is an electronic circuit that divides a given frequency by a factor of n, where n is an integer. Here a divide-by-4 circuit is used which divides the input frequency by 4. The frequency divider is made up of two parts - an astable multivibrator and a divide-by-4 counter. Frequency dividers are an integral part of communication and audio based systems like Frequency Synthesizers, RF devices, Communication.

The Frequency Divider is made up of an astable multivibrator and a divide-by-4 counter. The astable multivibrator generates a clock signal of a specific frequency which is used as an input in the counter. Then the counter produces an output signal of a divide-by-4 frequency.

The Astable Multivibrator is also called a free-running multivibrator. It has two quasi-stable states and no external signal is required to produce the changes in state. The component values are used to decide the time for which circuit remains in each state. Usually, as the astable multivibrator oscillates between two states, is used to produce a square wave. In this circuit, the time period is dependent upon the value of the resistor and capacitor. It also depends upon the upper and lower threshold voltage of the op-amp.

Working in Detail

In the op-amp multivibrator circuit, the op-amp works as an analogue comparator. An op-amp comparator compares the voltages on its two inputs and gives a positive or negative output depending on whether the input is greater or less than some reference value, VREF.

However, because the open-loop op-amp comparator is very sensitive to the voltage changes on its inputs, the output can switch uncontrollably between its positive, +V(sat) and negative, -V(sat) supply rails whenever the input voltage being measured is near to the reference voltage, VREF.

The op-amp comparator circuit is configured as a Schmitt trigger that uses positive feedback of resistors R3 and R4 to generate hysteresis. As the two resistors are configured across the op-amp's output as a voltage divider network, the reference voltage, Vref will be dependent upon the fraction of output voltage fed back to the non-inverting input. This feedback fraction, β is given as:

Where +V(sat) is the positive op-amp DC saturation voltage and -V(sat) is the negative op-amp DC saturation voltage.

Then we can see that, +Vref = +V(sat)β -Vref = -V(sat)β

Let's assume that the capacitor is fully discharged and the output of the op-amp is saturated at the positive supply rail. The capacitor, C starts to charge up from the output voltage, Vout through a resistor, R at a rate determined by their RC time constant.

The capacitor wants to charge up to the value of Vout within five-time constants. However, as soon as the capacitor's charging voltage at the op-amp's inverting (-) terminal is equal to or greater than the voltage at the non-inverting terminal, the output will change state and be driven to the opposing negative supply rail.

But the capacitor, which was charging towards the positive supply rail (+V(sat)), now has a negative voltage, -V(sat) across its plates. This sudden reversal of the output voltage causes the capacitor to discharge toward the new value of Vout at a rate of the RC time constant.

Once the op-amps inverting terminal reaches the new negative reference voltage, -Vref at the non-inverting terminal, the op-amp once again changes state and the output is driven to the opposing supply rail voltage, +V(sat). The capacitor now has a positive voltage across its plates, and the charging cycle begins again. Thus, the capacitor is constantly charging and discharging creating an astable op-amp multivibrator output.

The period of the output waveform is determined by the RC time constant of the two-timing components and the feedback ratio established by the R3, R4 voltage divider network, which sets the reference voltage level. If the positive and negative values of the amplifiers saturation voltage have the same magnitude, then t1 = t2 and the expression to give the period of oscillation becomes:

Here: R is Resistance, C is Capacitance, ln( ) is the Natural Logarithm of the feedback fraction, T is periodic time in seconds, and ƒ is oscillation Frequency in Hz.

Then we can see from the above equation that the frequency of oscillation for an Op-amp Multivibrator circuit not only depends upon the RC time constant but also upon the feedback fraction.

A Divide-By-4 counter is a binary divider composed of two D flip flops where an inverted output terminal is connected back to the data terminal in a feedback loop. It is an asynchronous counter, where the first flip-flop is clocked by the external clock pulse and then each successive flip-flop is clocked by the output of the preceding flip-flop. As the signal moves in a ripple pattern, it takes some time at each stage resulting in the lower frequency at the output.

It is an Open Source EDA developed by FOSSEE, IIT Bombay. It is used for electronic circuit simulation. It is made by the combination of two software namely NgSpice and KiCAD.
For more details refer:
https://esim.fossee.in/home

It is an Open Source Software for Spice Simulations. For more details refer:
http://ngspice.sourceforge.net/docs.html

It is an Online Web Browser IDE for Verilog/System-verilog/TL-Verilog Simulation. Refer
https://www.makerchip.com/

It is a tool which converts Verilog code to C++ objects. Refer: https://www.veripool.org/verilator/

The following is the schematic in eSim:

`include "ff.v"
module counter(CLK, COUNT); 
 	
	input CLK; 
	output COUNT; 
	 
	reg CLK; 
	reg COUNT;

	wire C1; 
	wire Q1; 
	wire Q2; 
	 
	FF TFF1(.CLK(CLK), .Q(Q1), .QBAR(C1)); 
	FF TFF2(.CLK(C1), .Q(), .QBAR(Q2)); 
	 
	assign COUNT = Q2; 
 
endmodule 

module FF(CLK, Q, QBAR); 
 
	input CLK; 
 
	output QBAR; 
	output Q; 
 
	wire CLK; 
	wire Q; 
	wire QBAR; 
	 
	reg state; 
	 
	always @(posedge CLK) 
	begin 
		begin 
			state <= ~state; 
		end 
	end 
	 
	assign QBAR = ~state; 
	assign Q = state; 
 
endmodule 

`include "counter.v"
module tb; 
 
	reg CLK; 
	reg COUNT; 
	 
	counter counter1(.CLK(CLK), .COUNT(COUNT));
   
	always 
	begin 
      
		CLK = 0; 
		#2.5; 
     
		CLK = 1; 
      		#2.5; 
	end 
endmodule

\TLV_version 1d: tl-x.org
\SV
/* verilator lint_off UNUSED*/  /* verilator lint_off DECLFILENAME*/  /* verilator lint_off BLKSEQ*/  /* verilator lint_off WIDTH*/  /* verilator lint_off SELRANGE*/  /* verilator lint_off PINCONNECTEMPTY*/  /* verilator lint_off DEFPARAM*/  /* verilator lint_off IMPLICIT*/  /* verilator lint_off COMBDLY*/  /* verilator lint_off SYNCASYNCNET*/  /* verilator lint_off UNOPTFLAT */  /* verilator lint_off UNSIGNED*/  /* verilator lint_off CASEINCOMPLETE*/  /* verilator lint_off UNDRIVEN*/  /* verilator lint_off VARHIDDEN*/  /* verilator lint_off CASEX*/  /* verilator lint_off CASEOVERLAP*/  /* verilator lint_off PINMISSING*/  /* verilator lint_off BLKANDNBLK*/  /* verilator lint_off MULTIDRIVEN*/  /* verilator lint_off WIDTHCONCAT*/  /* verilator lint_off ASSIGNDLY*/  /* verilator lint_off MODDUP*/  /* verilator lint_off STMTDLY*/  /* verilator lint_off LITENDIAN*/  /* verilator lint_off INITIALDLY*/

//Your Verilog/System Verilog Code Starts Here:
module tb; 
 
	reg CLK; 
	reg COUNT; 
	 
	counter counter1(.CLK(CLK), .COUNT(COUNT));
   
	always 
	begin 
      
		CLK = 0; 
		#2.5; 
     
		CLK = 1; 
      		#2.5; 
	end 
 
endmodule

//Top Module Code Starts here:	
module FF(CLK, Q, QBAR); 
 
	input CLK; 
 
	output QBAR; 
	output Q; 
 
	wire CLK; 
	wire Q; 
	wire QBAR; 
	 
	reg state; 
	 
	always @(posedge CLK) 
	begin 
		begin 
			state <= ~state; 
		end 
	end 
	 
	assign QBAR = ~state; 
	assign Q = state; 
 
endmodule 

module counter(CLK, COUNT); 
 
	input CLK; 
	output COUNT; 
	 
	wire CLK; 
	wire COUNT; 
	 
	wire C1; 
	wire Q1; 
	wire Q2; 
	 
	FF TFF1(.CLK(CLK), .Q(Q1), .QBAR(C1)); 
	FF TFF2(.CLK(C1), .Q(), .QBAR(Q2)); 
	 
	assign COUNT = Q2;
 
endmodule 

module top(input logic clk, input logic reset, input logic [31:0] cyc_cnt, output logic passed, output logic failed);
	logic COUNT;		
   counter counter1(.CLK(clk), .COUNT(COUNT));
endmodule

• Operating Voltage of the circuit is 5V
• Clock Signal frequency generated by Astable Multivibrator is 2.6KHz
• β of the circuit is 0.909
• Theoretical Output Frequency of the circuit is 650Hz
• Output Frequency achieved by the circuit is 645Hz

1. Open eSim
2. Run NgVeri-Makerchip
3. Add top level verilog file in Makerchip Tab
4. Click on NgVeri tab
5. Add dependency files
6. Click on Run Verilog to NgSpice Converter
7. Debug if any errors
8. Model created successfully

1. Open a new terminal
2. Clone this project using the following command:
   git clone https://github.com/PatelVatsalB21/Mixed_Signal_Frequency_Divider.git
   
3. Change directory:
   cd frequency_divider
   
4. Run ngspice:
   ngspice Frequency_Divider.cir.out
   
5. To run the project in eSim:

• Run eSim
  
• Load the project
  
• Open eeSchema
  

• FOSSEE, IIT Bombay
• Steve Hoover, Founder, Redwood EDA
• Kunal Ghosh, Co-founder, VSD Corp. Pvt. Ltd. - kunalpghosh@gmail.com
• Sumanto Kar, eSim Team, FOSSEE

• Op-amp Astable Multivibrator
• Frequency Division Using Flip Flops