Ring Oscillator Calculator
Estimate conventional digital inverter ring oscillator frequency from an odd number of inverting stages and finite propagation delay. The calculator supports average-delay analysis, tPLH/tPHL analysis, target-delay solving, valid odd stage-count recommendation, delay sensitivity, and PVT delay corners.
OSC-010 is distinct from DIG-010: a ring oscillator creates a clock from propagation delay and odd inversion, while a frequency divider takes an existing clock and divides it.
Engineering tool
Ring Oscillator Calculator
Estimate conventional inverter ring oscillator frequency from odd stage count and propagation delay.
Calculation mode
Parameter panel
Result console
- Oscillation Frequency
- 10 MHz
- Oscillation Period
- 100 ns
- Loop Propagation Delay
- 50 ns
- Full-Cycle Delay
- 100 ns
- Average Stage Delay
- 10 ns
- Stage Count
- 5
- Inversions
- 5
- Transitions per Period
- 2
Ring oscillator formula audit
| Adopted Topology | Conventional digital inverter ring oscillator. |
|---|---|
| Stage Definition | One inverting delay stage with finite propagation delay. |
| Minimum Stage Count | Odd integer N >= 3 for a conventional inverter ring. |
| Odd-Stage Requirement | Even inverter loops do not represent the standard self-oscillating topology. |
| Propagation Delay | Input crossing to output crossing delay, not rise time or fall time. |
| tPLH Definition | Output low-to-high propagation delay. |
| tPHL Definition | Output high-to-low propagation delay. |
| Average Delay | tpd = (tPLH + tPHL)/2. |
| Loop Delay | tloop = N tpd. |
| Period Formula | T = 2Ntpd. |
| Frequency Formula | f = 1/(2Ntpd). |
| Separate-Delay Formula | T = N(tPLH + tPHL). |
| Stage Count Solver | Nideal = 1/(2 f tpd), then compare valid odd integer designs. |
| Sensitivity Model | fnew/f0 = tpd0/tpd,new. |
| PVT Model | Frequency corners are computed from entered delay corners only. |
| Duty-Cycle Boundary | Duty cycle is not modeled from tPLH/tPHL in V1. |
| Loading Boundary | Load capacitance and fan-out are represented only by their effect on entered delay. |
| Startup Boundary | Odd inversion is required, but real startup still depends on analog device behavior and noise. |
Formula reference
Ring Oscillator Formulas
The V1 model is a first-order digital timing estimate for a conventional inverter ring. It does not model transistor sizing, jitter, phase noise, or extracted routing capacitance.
tpd = (tPLH + tPHL) / 2tloop = N tpdT = 2Ntpdf = 1 / (2Ntpd)T = N(tPLH + tPHL)tpd = 1 / (2Nf)Nideal = 1 / (2ftpd)tPHL = 1/(Nf) - tPLHfnew/f0 = tpd0/tpd,newVariable definitions
- N
- odd number of inverting stages
- tpd
- average propagation delay per stage
- tPLH
- output low-to-high propagation delay
- tPHL
- output high-to-low propagation delay
- tloop
- one transition around the loop
- T
- full HIGH-to-LOW-to-HIGH oscillation period
- f
- oscillation frequency
Ring Oscillator Formula Audit
| Adopted Topology | Conventional inverter ring oscillator. |
|---|---|
| Stage Definition | One inverting delay cell with finite propagation delay. |
| Minimum Stage Count | Odd integer N >= 3. |
| Odd-Stage Requirement | A conventional inverter ring oscillator requires an odd number of inversions. |
| Propagation Delay Definition | Input crossing to output crossing delay, not rise/fall time. |
| tPLH Definition | Output low-to-high propagation delay. |
| tPHL Definition | Output high-to-low propagation delay. |
| Average Delay Formula | tpd = (tPLH + tPHL)/2. |
| Loop Delay | tloop = Ntpd. |
| Period Formula | T = 2Ntpd. |
| Frequency Formula | f = 1/(2Ntpd). |
| Separate-Delay Formula | T = N(tPLH + tPHL). |
| Target Delay Solver | tpd = 1/(2Nf). |
| Complementary Delay Solver | tPHL = 1/(Nf) - tPLH, or tPLH = 1/(Nf) - tPHL. |
| Stage Count Solver | Nideal = 1/(2ftpd), then compare valid odd integer choices. |
| Sensitivity Model | fnew/f0 = tpd0/tpd,new. |
| Tolerance / PVT Model | Minimum frequency uses maximum entered delay; maximum frequency uses minimum entered delay. |
| Duty-Cycle Boundary | No universal duty-cycle formula is asserted from tPLH/tPHL in V1. |
| Loading Boundary | Fan-out, routing and probe capacitance are represented only by entered delay. |
| Startup Boundary | Odd inversion is necessary for the conventional topology, but real startup also depends on analog device behavior and noise. |
Worked Examples
3-stage frequency
Known: N = 3, tpd = 10 ns
T = 2 x 3 x 10 ns = 60 ns, f = 16.6667 MHz.
5-stage frequency
Known: N = 5, tpd = 10 ns
T = 100 ns, f = 10 MHz.
7-stage frequency
Known: N = 7, tpd = 10 ns
f = 1/(140 ns) = 7.142857 MHz.
Separate delays
Known: N = 5, tPLH = 8 ns, tPHL = 12 ns
tpd = 10 ns, T = 5(8 + 12) ns = 100 ns, f = 10 MHz.
Formula equivalence
Known: Same separate-delay case
2Ntpd equals N(tPLH + tPHL).
Solve tpd
Known: Target f = 10 MHz, N = 5
tpd = 1/(2Nf) = 10 ns.
Faster target
Known: Target f = 20 MHz, N = 5
tpd = 5 ns.
Exact stage count
Known: Target f = 10 MHz, tpd = 10 ns
Nideal = 5, which is a valid odd stage count.
Even ideal count
Known: Nideal = 8
Compare N = 7 and N = 9; do not use an 8-stage conventional inverter ring.
Invalid even N
Known: N = 4
Rejected because a conventional inverter ring requires odd N.
Invalid N = 1
Known: N = 1
Rejected for ordinary inverter ring oscillator design.
Invalid fractional N
Known: N = 3.5
Rejected because stage count must be an integer.
Delay scaling
Known: tpd doubles
Frequency halves for fixed stage count.
+10% delay
Known: tpd,new = 1.1tpd
Frequency shift is 1/1.1 - 1 = -9.09%, not exactly -10%.
-10% delay
Known: tpd,new = 0.9tpd
Frequency shift is 1/0.9 - 1 = +11.111%.
Solve tPHL
Known: Target 10 MHz, N = 5, tPLH = 8 ns
tPHL = 12 ns.
Invalid complementary delay
Known: Known delay exceeds 1/(Nf)
Rejected instead of returning negative delay.
Unit conversion
Known: 1000 ps = 1 ns
Both inputs produce identical frequency.
Frequency units
Known: 1000 kHz = 1 MHz
Target-delay solver returns the same delay.
PVT corners
Known: tpd min = 9 ns, nominal = 10 ns, max = 11 ns
fmax > fnominal > fmin.
Engineering Notes
| Ring Oscillator | A ring oscillator creates a clock from a loop of inverting delay stages. |
|---|---|
| Odd Number of Stages | A conventional inverter ring requires odd N and normally N >= 3. |
| Propagation Delay | Use input-to-output propagation delay from the relevant logic family and load condition. |
| tPLH / tPHL | Separate delays can be averaged for frequency, but V1 does not claim a universal duty-cycle result. |
| PVT | Process, voltage, temperature and loading change stage delay and therefore frequency. |
| Supply Voltage | Supply changes delay and can pull the oscillator frequency. |
| Load Capacitance | Fan-out, routing capacitance and probing usually increase delay and lower frequency. |
| Buffering | Measurement should usually be taken through a buffer to avoid loading the ring node. |
| Jitter | Jitter and phase noise require device-level or measured data and are not predicted here. |
| Frequency Divider Boundary | DIG-010 divides an existing clock. OSC-010 creates an approximate clock from delay stages. |
Common Mistakes
- Using an even number of inverter stages.
- Allowing N = 1 as an ordinary ring oscillator.
- Forgetting the factor of two in the period.
- Using f = 1/(Ntpd) for a full cycle.
- Using rise time as propagation delay.
- Reversing tPLH and tPHL definitions.
- Averaging separate delays incorrectly.
- Rounding target stage count to an even number.
- Assuming a target frequency can always be exact.
- Treating +10% delay as exactly -10% frequency.
- Ignoring PVT variation.
- Ignoring load capacitance and fan-out.
- Probing the ring node directly.
- Confusing a ring oscillator with a frequency divider.
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Support reference
FAQ
What is a ring oscillator?
A ring oscillator is a loop of inverting delay stages. With an odd number of inversions and finite propagation delay, the loop cannot settle into a static logic state and oscillates.
How do I calculate ring oscillator frequency?
For a conventional inverter ring using average per-stage propagation delay, use f approximately equal to 1/(2Ntpd), where N is the odd stage count and tpd is average propagation delay.
Why does a ring oscillator need an odd number of inverters?
An odd number of inversions provides the logical inversion around the loop. A conventional even-stage inverter loop is not the standard self-oscillating topology.
Why is the frequency approximately 1/(2Ntpd)?
One transition takes about N times tpd to propagate around the loop. A full HIGH to LOW to HIGH cycle requires two loop propagations, so T is about 2Ntpd.
What is propagation delay?
Propagation delay is the time from an input logic threshold crossing to the corresponding output logic threshold crossing.
What is the difference between tPLH and tPHL?
tPLH is output low-to-high propagation delay, while tPHL is output high-to-low propagation delay. Their average is commonly used as tpd.
Can I use rise time and fall time instead?
No. Rise and fall time describe output edge transition duration. They are not the same as propagation delay.
How do I calculate the required propagation delay for a target frequency?
Use tpd = 1/(2Nf) with a valid odd stage count N.
How do I choose the number of stages?
Calculate Nideal = 1/(2ftpd), then compare the nearest lower and higher valid odd stage counts. The target may not be exact because N is discrete.
Why can't I use an even number of inverter stages?
A conventional inverter ring oscillator requires an odd number of inverting stages. Even-stage loops have different logic behavior and are not modeled here.
How does supply voltage affect ring oscillator frequency?
Supply voltage changes logic gate propagation delay. Higher or lower supply can shift frequency depending on the device family and operating region.
How does temperature affect frequency?
Temperature changes device speed and propagation delay. The calculator only uses delay values or delay corners supplied by the user.
How does load capacitance affect frequency?
Additional load capacitance usually increases propagation delay and lowers frequency. The calculator does not derive delay from capacitance in V1.
Why should a ring oscillator be buffered before measurement?
Direct probing can load an oscillator node and shift its frequency. A buffer isolates the ring from measurement capacitance and external loading.
What is the difference between a ring oscillator and a frequency divider?
A ring oscillator creates a clock from propagation delay and odd inversion. A frequency divider takes an existing clock and divides it by an integer or counter chain.
Engineering Disclaimer
This calculator provides first-order digital ring oscillator timing estimates. Real devices require logic-family datasheets, extracted load capacitance, supply and temperature characterization, layout review, buffering, simulation, and measurement.