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In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. Typically, in analog electronics, these values are 10% and 90% of the step height: in control theory applications, according to Template:Harvtxt, rise time is defined as "the time required for the response to rise from x% to y% of its final value", with 0%-100% rise time common for underdamped second order systems, 5%-95% for critically damped and 10%-90% for overdamped. The output signal of a system is characterized also by fall time: both parameters depend on rise and fall times of input signal and on the characteristics of the system.

Overview

Rise time is an analog parameter of fundamental importance in high speed electronics, since it is a measure of the ability of a circuit to respond to fast input signals. Many efforts over the years have been made to reduce the rise times of generators, analog and digital circuits, measuring and data transmission equipment, focused on the research of faster electron devices and on techniques of reduction of stray circuit parameters (mainly capacitances and inductances). For applications outside the realm of high speed electronics, long (compared to the attainable state of the art) rise times are sometimes desirable: examples are the dimming of a light, where a longer rise-time results, amongst other things, in a longer life for the bulb, or digital signals apt to the control of analog ones, where a longer rise time means lower capacitive feedthrough, and thus lower coupling noise.

Simple examples of calculation of rise time

The aim of this section is the calculation of rise time of step response for some simple systems: all notations and assumptions required for the following analysis are listed here.

• $t_{r}\,$ is the rise time of the analyzed system, measured in seconds.

• $f_{L}\,$ is the low frequency cutoff (-3 dB point) of the analyzed system, measured in hertz.

• $f_{H}\,$ is high frequency cutoff (-3 dB point) of the analyzed system, measured in hertz.

• $h(t)\,$ is the impulse response of the analyzed system in the time domain.

• $H(\omega )\,$ is the frequency response of the analyzed system in the frequency domain.

• The bandwidth is defined as

$BW=f_{H}-f_{L}\,$

and since the low frequency cutoff $f_{L}$ is usually several decades lower than the high frequency cutoff $f_{H}$,

$BW\cong f_{H}\,$

• All systems analyzed here have a frequency response which extends to 0 (low-pass systems), thus

$f_{L}=0\,\Leftrightarrow \,f_{H}=BW$ exactly.

• All systems analyzed are thought as electrical networks and all the signals are thought as voltages for the sake of simplicity: the input is a step function of $V_{0}$ volts.

Gaussian response system

A system is said to have a Gaussian response if it is characterized by the following frequency response

$|H(\omega )|=e^{-{\frac {\omega ^{2}}{\sigma ^{2}}}}$

where $\sigma >0$ is a constant, related to the high frequency cutoff by the following relation:

$f_{H}={\frac {\sigma }{2\pi }}{\sqrt {\frac {3}{20\log e}}}\cong 0.0935\sigma$

The corresponding impulse response can be calculated using the inverse Fourier transform of the shown frequency response

${\mathcal {F}}^{-1}\{H\}(t)=h(t)={\frac {1}{2\pi }}\int \limits _{-\infty }^{+\infty }{e^{-{\frac {\omega ^{2}}{\sigma ^{2}}}}e^{i\omega t}}d\omega ={\frac {\sigma }{2{\sqrt {\pi }}}}e^{-{\frac {1}{4}}\sigma ^{2}t^{2}}$

Applying directly the definition of step response

$V(t)=V_{0}{H*h}(t)={\frac {V_{0}}{\sqrt {\pi }}}\int \limits _{-\infty }^{\frac {\sigma t}{2}}e^{-\tau ^{2}}d\tau ={\frac {V_{0}}{2}}\left[1+\mathrm {erf} \left({\frac {\sigma t}{2}}\right)\right]\Leftrightarrow {\frac {V(t)}{V_{0}}}={\frac {1}{2}}\left[1+\mathrm {erf} \left({\frac {\sigma t}{2}}\right)\right]$

Solving for t's the two following equations by using known properties of the error function

$0.1={\frac {1}{2}}\left[1+\mathrm {erf} \left({\frac {\sigma t_{1}}{2}}\right)\right]\qquad 0.9={\frac {1}{2}}\left[1+\mathrm {erf} \left({\frac {\sigma t_{2}}{2}}\right)\right]$

the value $t=-t_{1}=t_{2}$ is then known and since $t_{r}=t_{2}-t_{1}=2t$

$t_{r}={\frac {4}{\sigma }}{\mathrm {erf} ^{-1}(0.8)}\cong {\frac {0.3394}{f_{H}}}$

and then

$t_{r}\cong {\frac {0.34}{BW}}\quad \Longleftrightarrow \quad BW\cdot t_{r}\cong 0.34$

One stage low pass RC network

For a simple one stage low pass RC network, the 10% to 90% rise time is proportional to the network time constant $\tau =RC$:

$t_{r}\cong 2.197\tau \,$

The proportionality constant can be derived by using the output response of the network to a unit step function input signal of $V_{0}$ amplitude, aka its step response:

$V(t)=V_{0}\left(1-e^{-{\frac {t}{\tau }}}\right)$

Solving for t's

${\frac {V(t)}{V_{0}}}=\left(1-e^{-{\frac {t}{\tau }}}\right)$

${\frac {V(t)}{V_{0}}}-1=-e^{-{\frac {t}{\tau }}}$

$1-{\frac {V(t)}{V_{0}}}=e^{-{\frac {t}{\tau }}}$

$\ln \left(1-{\frac {V(t)}{V_{0}}}\right)=-{\frac {t}{\tau }}$

$t=-\tau \;\ln \left(1-{\frac {V(t)}{V_{0}}}\right)$

We call t₁ the time needed to go from 0% to 10% of the steady-state value, and t₂ the one to 90%. Thus t₁ is such that ${\frac {V(t)}{V_{0}}}=0.1$ and t₂ is such that ${\frac {V(t)}{V_{0}}}=0.9$. Solving the previous equation for these two values we find the analitical expression for t₁ and t₂:

$t_{1}=-\tau \;\ln \left(1-0.1\right)=-\tau \;\ln \left(0.9\right)=-\tau \;\ln \left({\frac {9}{10}}\right)=\tau \;\ln \left({\frac {10}{9}}\right)=\tau ({\ln 10}-{\ln 9})$

We obtain t₂ in the same way, resulting in

$t_{2}=\tau \ln {10}\,$

Subtracting $t_{1}$ from $t_{2}$ we obtain the rise time, whis is therefore proportional to the time constant:

$t_{r}=t_{2}-t_{1}=\tau \cdot \ln 9\cong \tau \cdot 2.197$

Now, noting that

$\tau =RC={\frac {1}{2\pi f_{H}}}$

(see here for the proof of the previous equation) then

$t_{r}\cong {\frac {2.197}{2\pi f_{H}}}\cong {\frac {0.349}{f_{H}}}$

and since the high frequency cutoff is equal to the bandwidth

$t_{r}\cong {\frac {0.35}{BW}}\quad \Longleftrightarrow \quad BW\cdot t_{r}\cong 0.35$

This formula implies that if the bandwidth of an oscilloscope is 350 MHz, its 10% to 90% risetime is 1 nanosecond.

Rise time of cascaded blocks

Consider a system composed by $n$ cascaded non interacting blocks, each having a rise time $\scriptstyle {t_{r_{i}}}$ and no overshoot in their step response: suppose also that the input signal of the first block has a rise time whose value is $\scriptstyle {t_{r_{S}}}$. Then its output signal has a rise time $\scriptstyle {t_{r_{O}}}$ equal to

$t_{r_{O}}={\sqrt {t_{r_{S}}^{2}+t_{r_{1}}^{2}+\dots +t_{r_{n}}^{2}}}$

This result is a consequence of the central limit theorem, as reported in Template:Harvnb and proved by Henry Wallman in Template:Harvnb.

Factors affecting rise time

Rise time values in a resistive circuit are primarily due to stray capacitance and inductance in the circuit. Because every circuit has not only resistance, but also capacitance and inductance, a delay in voltage and/or current at the load is apparent until the steady state is reached. In a pure RC circuit, the output risetime (10% to 90%), as shown above, is approximately equal to $2.2RC$.

Rise time in control applications

In control theory, for overdamped systems, rise time is commonly defined as the time for a waveform to go from 10% to 90% of its final value.

The quadratic approximation for normalized rise time for a 2nd-order system, step response, no zeros is:

$t_{r}\cdot \omega _{0}=2.230\zeta ^{2}-0.078\zeta +1.12\,$

where ζ is the damping ratio and ω₀ is the natural frequency of the network.

However, the proper calculation for rise time from 0 to 100% of an under-damped 2nd-order system is:

$t_{r}\cdot \omega _{0}={\frac {1}{\sqrt {1-\zeta ^{2}}}}\left(\pi -\tan ^{-1}\left({\frac {\sqrt {1-\zeta ^{2}}}{\zeta }}\right)\right)$

where ζ is the damping ratio and ω₀ is the natural frequency of the network.

See also

• Fall time
• Frequency response
• Impulse response
• Step response
• Transition time
• Settling time

Notes

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References

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  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
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  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• United States Federal Standard 1037C: Glossary of Telecommunications Terms
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 Paragraph 2 of chapter 2 and paragraphs 1 to 7 of chapter 7 .
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.