A circuit that combines two or more signals is called a mixer. In this lab, your goal is to build a mixer that combines the signals generated by two voltage sources, V1 and V2, where:
V1 is a 1 kHz square wave that varies between 0V and +1V, and
V2 is a 5 kHz sine wave that varies between -1V and +1V.
Please design a circuit that mixes V1 and V2 to produce Vout such that
Vout≈12V1+16V2.
The resulting output should be similar to that shown in Figure 1. The maximum value of the output is approximately 667mV and the minimum value is approximately −167mV.
Enter your circuit below, using the appropriate configuration of resistors. Please do not modify the wiring or parameters of the voltage sources -- your goal is to take the signals they generate and combine them, not to change what is generated. Run a 5ms transient analysis to verify the correct operation of your circuit. We will be checking for the transient waveform at the "output" node.
The min value of 12V1 is 0
the min value of 16V2 is less than -16*1.4
so the min value of 12V1+16V2 is about -16*1.4
So I am wondering exactly about this statement: Vout≈12V1+16V2.
The resulting output should be similar to that shown in Figure 1. The maximum value of the output is approximately 667mV and the minimum value is approximately −167mV.
Consider a deuteron in a cyclotron with field strength 0.5T. The deuteron is accelerated twice per rotation by a potential of V=25 kV. (a) If the radius of the cyclotron is 2 meter, what is the maximum energy of the deuteron? Express your answer in Joules (the deuteron mass is 3.34×10−27kg) b)Starting from a negligibly small velocity, how many full rotations does the deuteron need before it reaches this maximum energy? c) What is the time it takes for the deuteron to make one complete rotation when its energy is about 500 keV and when it is about 5 MeV? Ignore possible relativistic effect
I have b) 500
Anyone for a) and c)?
Disappointed
To create a circuit that mixes the signals V1 and V2 to produce Vout, we can use an operational amplifier (op-amp) as a summing amplifier. The op-amp will add the weighted sum of the inputs V1 and V2 according to the equation Vout = 12V1 + 16V2.
Here's a circuit diagram that shows how to build the mixer using an op-amp:
```
+---------------------+
| |
V1 -----| |
| R1 |
+---/\/\/\--+--- |
| | |
+--|+ \ |
| | ) |
/ \ | | |
V2 ----- R2 ----/ \-------+--|---- Vout
\ / |
| |
| |
+-------------+
```
In this circuit, two resistors (R1 and R2) are used to weight the inputs V1 and V2, respectively. The output of the op-amp is taken from the junction between the two resistors.
To determine the values of R1 and R2, we can use the equation Vout = 12V1 + 16V2. Since V1 varies between 0V and +1V, and V2 varies between -1V and +1V, we need to make sure that the maximum output voltage is approximately 667mV and the minimum output voltage is approximately -167mV.
Let's calculate the resistor values:
For the maximum output voltage of 667mV:
Vout = 12V1 + 16V2
0.667 = 12(1) + 16(1)
0.667 = 12 + 16
0.667 = 28
28 = R1 + R2
For the minimum output voltage of -167mV:
Vout = 12V1 + 16V2
-0.167 = 12(0) + 16(-1)
-0.167 = -16
16 = R1 + R2
Solving these two equations simultaneously, we can find the values of R1 and R2:
28 = R1 + R2
16 = R1 + R2
By subtracting 16 from both sides of the second equation, we get:
12 = R1
Substituting this value into either of the original equations, we find:
R1 = 12
R2 = 28 - R1 = 28 - 12 = 16
So, the values for R1 and R2 are 12Ω and 16Ω, respectively.
Once the circuit is built, you can perform a 5ms transient analysis to verify the correct operation. The resulting waveform at the "output" node should resemble the given waveform in Figure 1, with a maximum value of approximately 667mV and a minimum value of approximately -167mV.