# Regarding AC Analysis

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#### Hanumantas

##### Newbie level 4 Hello All,

We have 3 basic analysis for a electronics circuits: DC Analysis, AC Analysis and Transient Analysis.

DC Analysis: Used to get the DC Operating point(Constant Voltage and Current) by making Capacitance OPEN and Inductance SHORT.

I have some confusion in AC Analysis, which is said to be small signal analysis by sweeping frequencies of the input signal.
For AC Analysis:
1. We first calculate the DC operating point by DC Analysis.
2. For small signal analysis, we assume linear behaviour near the DC Operating point. But in Simulator we can make input signal vary from 1mvolt to 100volts and we get the bode plot for that. But as we say small signal model is only valid for small signal which see the small part of Output Current/Input Voltage curve linear across DC operating point. Then why does we can be able to feed large signal of several volts in AC analysis.

I have this doubt of AC analysis with its concept of small signal analysis. Please do explain with respect to simulators LTspice or by concept..

#### LvW 2. For small signal analysis, we assume linear behaviour near the DC Operating point. But in Simulator we can make input signal vary from 1mvolt to 100volts and we get the bode plot for that. But as we say small signal model is only valid for small signal which see the small part of Output Current/Input Voltage curve linear across DC operating point. Then why does we can be able to feed large signal of several volts in AC analysis.

"Small signal" analysis means: Each signal (each voltage) will be treated as if it would be a small signal - not leaving the quasi-linear region of the device. Example: For a BJT the slope around the bias point is calculated and used as a gain factor - independent if you apply 1mV or 1000 volts. Of course, in reality you have to take into account all non-linearities which are covered by the Tran analysis.
Therefore, the ac analysis primarily is used to find the transfer function of a circuit, which - by definition - is a linear one.

• keith1200rs and Hanumantas

Points: 2

### keith1200rs

Points: 2

#### Hanumantas

##### Newbie level 4 Lets take an example, a circuit with Resistor R and Diode D. For small signal analysis,, the non linearity of D is made linear by Linear components R here by using DC loadline, thus we get the DC Operating point. Now at small region across this point we assume linearity, but its very small region where our assumtion of linearity of circuit holds good in Output Current/Input Voltage curve. If we supply, a big amplitude signal then it will face the non linearity as Then how come it will be linear?

Also AC Analysis is used to see the response of Frequency sweep, means Observing the output for a signal with different frequency. It should show the non linearity, as Gain starts decreasing for a Low pass filter..

Please correct if I am wrong..

Thanks..

"Small signal" analysis means: Each signal (each voltage) will be treated as if it would be a small signal - not leaving the quasi-linear region of the device. Example: For a BJT the slope around the bias point is calculated and used as a gain factor - independent if you apply 1mV or 1000 volts. Of course, in reality you have to take into account all non-linearities which are covered by the Tran analysis.
Therefore, the ac analysis primarily is used to find the transfer function of a circuit, which - by definition - is a linear one.

#### keith1200rs

##### Super Moderator
Staff member LvW's explanation is a good one. With the example you have just given it still holds true. An AC analysis will assume a very small signal, never straying from the approximation that the transfer function is a straight line around the DC operating point. If you want to use a large signal you should not use the AC analysis - use transient analysis.

Keith

#### Hanumantas

##### Newbie level 4 Dear Keith,

Then why are we able to give input to this non-linear circuit from 1mV to 1000mV in LTspice Simulator. It should show some sort of error, as we are going out of non-linearity and it should suggest to use Tran analysis to avoid mis interpretation...

Thanks..

LvW's explanation is a good one. With the example you have just given it still holds true. An AC analysis will assume a very small signal, never straying from the approximation that the transfer function is a straight line around the DC operating point. If you want to use a large signal you should not use the AC analysis - use transient analysis.

Keith

#### keith1200rs

##### Super Moderator
Staff member It is not really a voltage simply a multiplier for the overall calculations. It does not affect the fact that the calculations will use the forward small signal transfer function around the DC operating point.

A normal value to use would be 1. That doesn't mean 1V but if the output is shown as 10V then the gain is 10. It is more useful to plot the output in dB in which case the output is gain if you used AC=1. I rarely use anything other than AC=1.

Keith

• Hanumantas

### Hanumantas

Points: 2

#### LvW Then why are we able to give input to this non-linear circuit from 1mV to 1000mV in LTspice Simulator. It should show some sort of error, as we are going out of non-linearity
Thanks..

Hanumantas, as I have mentioned - the signal (independent on its real value) is TREATED by the simulator as if it would be small enough to stay within the linear range of the part.
Or - other way round: The part is TREATED (idealized) as if it would have a linear transfer characteristic through its bias point. This is equivalent to a tangent drawn through the dc bias point.
The user of the simulator must know that the ac analysis does not recognize any non-linearity and that this particular analysis does nothing else than to use the SLOPE of the nonlinear characteristic for calculation.
Therefore, this analysis primarily is used for gain calculations or any other calculations which involve the RATIO of two quantities - like input or output resistances of amplifiers.
Counter example: It is not a good idea to use the ac analysis for calculating the current through a diode as function of the applied voltage (because the desired result is not a ratio of two parameters).

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Another explanation: The ac analysis does nothing else the you do with pencil and paper when you try to calculate currents and voltages in a linear network consisting of R, L, C .
In this case, the results also are independent on the sources and its (fictitious) values

#### FvM

##### Super Moderator
Staff member It should show some sort of error, as we are going out of non-linearity and it should suggest to use Tran analysis to avoid mis interpretation...
"Do you understand the nature of AC analysis? Otherwise review your text books"

Your diode example suggests that you're not yet aware of SPICE AC analysis operation. It simply doesn't care for signal magnitude and linearity. It calculates the DC operation point and determines differential impedances of all components at this point. Then it performs a linear AC analysis with this values. There's no need to check a particular voltage or current against any limit value.

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