Question

3. The picture below shows actual oscilloscope traces taken from the output of a function gen erator. The upper trace shows the signal when the generator is plugged directly into the oscilloscope; the lower trace shows the signal when a "tee" is attached to the input of the oscilloscope, and a 1502 resistor is hung on the tee, with the other end connected to ground, as shown in the sketch. From this information, determine the Thévenin equivalent circuit of the function generator: Express the Thévenin voltage as Vrh = Vo sin(2πft), and find values for both Vo and f, as well as the Thévenin resistance RTh for the generator. (Timebase set at 400μs/Div, vertical gain set at 5.00V/Div.) Hint: you can treat the oscilloscope as having an (almost) infinte resistance compared to the tee. Tek Run Function Generator Osciloscope TEE O O o 150 Ω

Answer 1

From the first oscilloscope trend (Function generator output directly connected to Oscilloscope) we will have following data:

Peak to Peak Voltage = 20V;

Zero to Peak Voltage; V₀ = 10V;

Time Period; T = 2*400us = 800 us

Frequency; f = 1/T = 1/(800us) = 1/(800 * 10^-6) Hz = 1250 Hz

V_th = V₀ sin(2πft) = 10 sin (2π * 1250 t)

V_th  = 10 sin (2500 π t)

Similarly we can find Voltage in second case when Tee circuit is connected as follows:

V_L = 7.5 sin (2500 π t)

Now, we need to find equivalent Thevenin Resistance (R_th) of Function generator

There will be same current from Function generator to 150 Ohm resistance & R_th (considering infinite input impedance of Oscilloscope) denoting as "I"

V_L = I * 150

I = V_L /150

Also, we can write,

V_TH = V_L + I * R_TH  

V_TH = V_L + V_L / 150 * R_TH  

V_TH = V_L (1 + R_TH / 150 )

(1 + R_TH / 150 ) =   V_TH / V_L = 10/7.5 (Using values of V_TH and V_L)

R_TH = 150 * [(4/3) -1 ]

R_TH = 50 Ohm