Hi All
I'm trying to get a better understanding of analysing circuits in the frequency domain. Attached are two circuits consisting of resistors and capacitors, and powered by a constant current source.
Figure 1: Here the resistor R1 and capacitor C1 are in parallel, so we can calculate the equivalent impedance \(Z_{eq}\) using
\(Z_{eq} = \frac{Z_{R1} Z_{C1}}{Z_{R1} + Z_{C1}}\)
where
\( Z_{R1} = R \) and \( Z_{C1} = \frac{1}{j\omega C} \)
which after substitution and rearranging gives
\(Z_{eq} = \frac{R}{1+j\omega RC}\)
Then, given that I know the frequency of the current source and its magnitude, I can simply apply Ohm's law to get \(V_1\), i.e.,
\(V_1 = I_1 Z_{eq}\)
I understand this. However, in Figure 2, I'm a little lost as to how to calculate the equivalent impedances if I want to calculate a value for \(V_2\). My initial attempt was to say R2 and C2 are in parallel and use the above method to calculate \(Z_{eq2}\), then to say R3 and C3 are in parallel to calculate \(Z_{eq3}\). This then forms a simple potential divider circuit where
\(V_2 = I_2\times \frac{Z_{eq3}}{Z_{eq2}+Z_{eq3}}\)
but this doesn't seem to work, i.e., the spice simulation doesn't match my calcs. Am I doing something fundamentally wrong by calculating the impedances in this manner?
Thanks for any tips.
I'm trying to get a better understanding of analysing circuits in the frequency domain. Attached are two circuits consisting of resistors and capacitors, and powered by a constant current source.
Figure 1: Here the resistor R1 and capacitor C1 are in parallel, so we can calculate the equivalent impedance \(Z_{eq}\) using
\(Z_{eq} = \frac{Z_{R1} Z_{C1}}{Z_{R1} + Z_{C1}}\)
where
\( Z_{R1} = R \) and \( Z_{C1} = \frac{1}{j\omega C} \)
which after substitution and rearranging gives
\(Z_{eq} = \frac{R}{1+j\omega RC}\)
Then, given that I know the frequency of the current source and its magnitude, I can simply apply Ohm's law to get \(V_1\), i.e.,
\(V_1 = I_1 Z_{eq}\)
I understand this. However, in Figure 2, I'm a little lost as to how to calculate the equivalent impedances if I want to calculate a value for \(V_2\). My initial attempt was to say R2 and C2 are in parallel and use the above method to calculate \(Z_{eq2}\), then to say R3 and C3 are in parallel to calculate \(Z_{eq3}\). This then forms a simple potential divider circuit where
\(V_2 = I_2\times \frac{Z_{eq3}}{Z_{eq2}+Z_{eq3}}\)
but this doesn't seem to work, i.e., the spice simulation doesn't match my calcs. Am I doing something fundamentally wrong by calculating the impedances in this manner?
Thanks for any tips.
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