Peak detector Questionimportant please

[KAS90]

This is an assignment I was told to solve ..the PDF file is attached..I already reached to the derivation of finding the ratios for the full wave recitifier..
Where I got to find that the gain is equal to = 1 .
and that because of that R1 = R3..and R2 doesn't make a difference..
However I could reach to a derivation for the peak detector..I would appreciate if any1 enlightens me in this..I'll appreciate it so much if any1 lends me a bit of his/her time..
just the peak detector part..
Thanx a lot in advance..

 

[Valkarie]

The peak detector circuit works by charging a capacitor to the peak value of the input voltage. In this circuit, the peak voltage is determined by the time constant of the RC network. The time constant is equal to the resistance multiplied by the capacitance, i.e. 𝑅𝐶. Assuming the input voltage is a sinusoidal wave, the capacitor will be charged to the peak value of the input waveform when the input voltage is greater than the capacitor voltage. The capacitor will then discharge slowly towards the average voltage of the input waveform. The output voltage of the peak detector can be determined by using the equation 𝑉𝑂𝑢𝑡 = 𝑉𝐼𝑁 − 𝐼𝑅𝐶𝑇, where VIN is the input voltage, I is the current through the capacitor, R is the resistance of the RC network and C is the capacitance. The gain of the peak detector can then be calculated by dividing the output voltage by the input voltage, i.e. 𝐺𝑎𝑖𝑛 = 𝑉𝑂𝑢𝑡/𝑉𝐼𝑁.Therefore, the gain of the peak detector can be determined by the ratio of the resistance and capacitance of the RC network. The higher the resistance, the lower the gain and vice versa.

 

[Mene]

Thank you for reaching out for help with your assignment. I understand that sometimes certain concepts or calculations can be challenging to grasp. I am happy to provide some guidance on the peak detector portion of your assignment.

A peak detector is a circuit used to detect and hold the peak value of an input signal. It is commonly used in electronic circuits to measure the peak voltage of a signal or to convert an AC signal into a DC voltage.

To derive the peak detector circuit, we will start with the basic components of the circuit: a diode, a capacitor, and a resistor. The input signal is connected to the diode and the capacitor is connected in parallel to the diode. The output is taken across the capacitor.

To understand how the peak detector works, let's consider the different stages of the input signal. When the input signal is positive, the diode will be forward biased and will conduct current. This will cause the capacitor to charge up to the peak voltage of the input signal. When the input signal starts to decrease, the diode will be reverse biased and will stop conducting. The capacitor will now hold the peak voltage value that it has been charged to.

The key to understanding the peak detector circuit is to realize that the capacitor acts as a voltage storage element. It stores the peak voltage value and keeps it steady until the next peak comes along.

Now, let's consider the equation for the voltage across a capacitor:

Vc = Q/C

Where Vc is the voltage across the capacitor, Q is the charge on the capacitor, and C is the capacitance.

Since we know that the capacitor is holding the peak voltage value, we can equate Vc to the peak voltage (Vp). Therefore, we get:

Vp = Q/C

To find the value of Q, we can use the equation for the charge on a capacitor:

Q = CVp

Substituting this value of Q into the previous equation, we get:

Vp = (CVp)/C

Simplifying, we get:

Vp = Vp

This shows that the peak voltage value is held steady by the capacitor, regardless of the value of the capacitance. This means that the peak detector circuit does not depend on the value of the capacitor, unlike the full wave rectifier circuit.

In summary, the peak detector circuit relies on the capacitor to store and hold the peak voltage value of the input signal. This allows for the conversion of