# Hv(jω) Magnitude Calculation in non-standard circuits.

In summary: The magnitude of the result is the magnitude response. The phase angle of the result is the phase response.In summary, the task at hand is to calculate the magnitude and phase response of a circuit that is neither Low-Pass, High Pass, nor Band-Pass. This can be done by using the commonly suggested methodology of finding the equivalent Thevenin impedance and voltage, and then substituting the numerical values for all the impedances in the expression and working out the arithmetic. The result will give the magnitude and phase response of the circuit.
I was wondering how to calculate the magnitude and phase response of any circuit that is neither Low-Pass,High Pass nor Band-Pass. I am asking this because i haven't found anything relevant in any textbooks so far , since the only use standard filters.

e.g an AC circuit consisting of an AC source with internal resistance A , capacitor C , inductor L , resistance B (the load) such that :

Zc||(Zb + ZL)

Following the commonly suggested methodology , the equivalent Thevenin impedance would be :

[ (jωL)-(ω*ω*L*C*Za) + Za ] / [ 1 + j*ω*C*Za ]

and the Thevenin Voltage :
Vthev = Vsource * ( Zc / (Zc + Za))

Therefore :

where Hv(jω) is the coefficient in front of Vsource which will be quite complicated.

How can we calculate its magnitude and phase response ?

Thank you

I was wondering how to calculate the magnitude and phase response of any circuit that is neither Low-Pass,High Pass nor Band-Pass. I am asking this because i haven't found anything relevant in any textbooks so far , since the only use standard filters.

e.g an AC circuit consisting of an AC source with internal resistance A , capacitor C , inductor L , resistance B (the load) such that :

Zc||(Zb + ZL)

Following the commonly suggested methodology , the equivalent Thevenin impedance would be :

[ (jωL)-(ω*ω*L*C*Za) + Za ] / [ 1 + j*ω*C*Za ]

and the Thevenin Voltage :
Vthev = Vsource * ( Zc / (Zc + Za))

Therefore :

where Hv(jω) is the coefficient in front of Vsource which will be quite complicated.

How can we calculate its magnitude and phase response ?

Thank you

This is just a simple network analysis problem. To do the calculation, just substitute the numerical values for all those impedances (Za, Zb, Zc, Zthev, Zload, etc.) into the expression and work out the arithmetic. The arithmetic will, of course, involve complex numbers.

## 1. How do I calculate the magnitude of Hv(jω) in a non-standard circuit?

The magnitude of Hv(jω) in a non-standard circuit can be calculated using the formula: |Hv(jω)| = √(Hv(jω) * Hv(-jω)). This involves finding the transfer function Hv(jω) and its complex conjugate Hv(-jω) and taking the square root of their product.

## 2. Can I use the same method to calculate Hv(jω) magnitude in any type of circuit?

Yes, the formula for calculating the magnitude of Hv(jω) in a non-standard circuit can be used in any type of circuit, as long as the transfer function Hv(jω) is known. This includes circuits with multiple stages, feedback loops, and non-linear elements.

## 3. What is the significance of Hv(jω) magnitude in circuit analysis?

Hv(jω) magnitude is an important parameter in circuit analysis as it represents the gain of the circuit at a specific frequency. It helps in understanding the behavior of the circuit and can be used to design and optimize circuits for specific frequency responses.

## 4. How does the magnitude of Hv(jω) in a non-standard circuit affect the circuit's performance?

The magnitude of Hv(jω) in a non-standard circuit determines the amount of amplification or attenuation of the input signal at a specific frequency. A higher magnitude indicates a stronger signal, while a lower magnitude indicates a weaker signal. This affects the overall performance of the circuit and can impact its functionality.

## 5. Are there any limitations to calculating Hv(jω) magnitude in non-standard circuits?

One limitation is that the formula for calculating Hv(jω) magnitude assumes that the circuit is linear, meaning the output is directly proportional to the input. If the circuit contains non-linear elements, the magnitude calculation may not accurately reflect the circuit's behavior. Additionally, some circuits may have a very complex transfer function, making it difficult to obtain an exact magnitude value.

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