differentiator is used in t.v.
The phase of an integrator is -90 degrees (or -π/2 radians), meaning it lags the input signal by a quarter of a cycle. In contrast, the phase of a differentiator is +90 degrees (or +π/2 radians), indicating that it leads the input signal by a quarter of a cycle. These phase shifts are fundamental characteristics that influence how these systems respond to different frequency components of input signals.
In a computer there are many A/D converters that put analog into digital. This signal is what is usually then led into an op amp which in the right configuration can be designed into an integrator or differentiator which is then used to solve differential equations.
It has to do with the fact that what's being plotted isn't a simple function, y = f(x), on an x-y grid, but rather a set of parametric equations plotted on a f(t)-g(t) grid where: x = f(t) is your input, and y = g(t) is your output. Specifically, for the differentiator: x = f(t) y = df/dt. For the integrator: x = f(t) y = ∫ f(t) dt. So, if your input is x = f(t) = sin(t), then your two outputs will be df/dt = cos(t) and ∫ sin(t) dt = -cos(t). That means your coordinate axes for the differentiator and the integrator will be the parametric equations x = sin(t), y = cos(t) and x = sin(t), y = -cos(t), respectively. I don't know if you've ever worked with parametric equations before, but suffice it to say, both of those sets of equations are parametric equations for a circle. I'll add a link to parametric equations below if you want to learn more.
Electronic Numerical Integrator And Computer.
ENIAC(Electronic Numerical Integrator and Computer)
phase shift in integrator is 180 degrees and phase shift in differentiator is 0 degrees
noise is a ac signal(high frequency range), as LPF allows only lower frequencies integrator is has more noise immunity than differentiator
for integrator time constant must be greater than 15T(T being the pulse width)
Because the capacitor is in series with the output. Vice versa for the integrator.
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A; An integrator will integrate or slowly change as a rapid input is applied. Differentiate will have just the opposite effect
The phase of an integrator is -90 degrees (or -π/2 radians), meaning it lags the input signal by a quarter of a cycle. In contrast, the phase of a differentiator is +90 degrees (or +π/2 radians), indicating that it leads the input signal by a quarter of a cycle. These phase shifts are fundamental characteristics that influence how these systems respond to different frequency components of input signals.
let us try.........
filter,servo control system,summing &difference application
A high pass circuit can act as a differentiator because it allows high frequency signals to pass through while attenuating low frequency signals. This property causes the output to respond more to the rate of change of the input signal, making it behave similar to a mathematical differentiator.
Differential equations can be solved using operational amplifiers (op-amps) by creating analog circuits that model the mathematical relationships described by the equations. By configuring op-amps in specific ways, such as integrators or differentiators, you can represent the operations of differentiation and integration. For instance, an integrator circuit can produce an output proportional to the integral of the input signal, while a differentiator can provide an output proportional to the derivative. These circuits can be combined to create solutions to complex differential equations in real-time.
the ideal differentiator has some limitations. The output is limited to the supply voltages, and since the differentiator is a noise-amplifying device, it suffers from excessive response to high-frequencies. Generally a practical differentiator is combined with a low-pass filter to smooth the high-frequency noise effects. Figure 6 shows some possible modifications to the ideal circuit. A large (over 1 MΩ) resistor Rx may be inserted in parallel with Cs and a very small ( 10 pF or less) capacitor Cx may be inserted in parallel with Rf.