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Tuned ECE3424
Exercise circuits
Vers 1.0
A tuned circuit is one which has a resonant frequency. This characteristic frequency is defined by a choice of components. It can be quite sharply tuned (strong resonance at a single frequency), for which we say that it has a high "Q" (quality factor). A high Q circuit has a low damping factor. Most of the receivers like the one you are constructing in your lab, or like you might use in other wireless applications, use such resonant circuits. Although there are a number of options for tuned circuits, the ones that are most common in RF applications are the simple RLC circuits. The basic RLC circuit is a topology of either of the forms represented by figure 1.1.
Figure 1.1(a) Series RLC topology
Figure 1.1(b) Parallel RLC topology
The resonant frequency relates primarily to the fact that energy will bounce back and forth between energy storage elements L and C at a characteristic frequency f0 . The frequency is defined by the magnitudes of the inductance L and the capacitance C and is
f 0 = 1 (2 LC )
(1.1)
The oscillation will have a damping factor . The damping factor will be of the form
= R /( 2 Ro ) = R0 /(2 R )
for the series topology and for the parallel topology
for which R0 represents the characteristic resistance of the LC pair defined as
R0 =
L C
(1.2)
So, for the above circuits shown (figures 1.1), you would find that f0 = 1.6MHz and R0 = 100. If you check out the damping factors, they will be 0.1 and 0.2, respectively for the series and parallel topologies shown in figure 1.1. A damping factor that is less than 1 is considered to be underdamped,
and will ring with a frequency that damps out exponentially with decay exp[-( 0 t)] as represented by figure 1.2a.
Figure 1.2a. Ringing oscillation with exponential decay The resonance `quality factor' is inverse to the damping (no big surprise, but note the factor of 2)
Q = 1 (2 )
(1.3)
whether series or parallel. The quality factor Q can be related to a resonance peak as
Q=
f0 f
(1.4)
where f is the 3db width of the resonance peak (as a function of frequency) , as represented by figure 1.2b
Figure 1.2(b) Resonance peak due to a tuned circuit. Note that the x-axis is logarithmic (= decade scale) That's probably all the detailing you have need to know about RLC circuits. But they are vitally important to all sorts of applications. We tune them to our performance needs by adjusting the values of R, L and C. You will encounter a few resonance peaks when you run the simulations and when you assess the tuned amplifiers in lab tests on your AM/FM receivers. 1. (15 pts) As your first exercise set up both of the basic RLC circuit forms as represented by figures 1-1(a) and 1-1(b) (same schematic. They don't have to be connected). The sources V1 and V2 should both be of type VAC and have amplitudes (ACMAG) of 1.0mV. Make screen copies of these circuits (you can use the Edit > copy-to-clipboard feature of pSpice) and identify them as your figures 1.1(a) and 1.1(b). Under the Analysis > setup menu set up the AC sweep for decade sweep type, and sweep parameters 501 pts/decade, sweep from 100kHz to 10MegHz. Execute the simulation and make a screen snapshot (figures 1.2(a) and 1.2(b)) of the plots of outputs Vo1 and Vo2 (separate plots). Take a measure of f0 and f (at the 3dB levels) and compare these to your calculated values in a short table (Table 1.1). 2. (10 pts) Replace the VAC sources with others of type VPULSE (or put the VPULSE in series with the AC source). Set the parameters of the VPULSE sources to provide a sharp (rise and fall times TR= TF = 0.1ns) 0 -> 1.0V pulse, of period 20us and pulse width = 15us. Make a transient sweep from 0 to 35us with step size =1.0ns. Execute the simulation and display the traces of Vo1 and Vo2, separate plots. From (either of) these identify traces the frequency of the ringing oscillation and the amplitude decay constant using your cursors. How do these compare with f0 and as represented by equations (1.1 and 1.3)? Include these values in your table (table 1.1). Make a snapshot of these traces (figures 1.3(a) and 1.3(b)) and include the cursor coordinate box showing your measurements. Note that you can accomplish these measure of both f0 and with just two cursor measurements. Include these measurements in your table also, along with the appropriate calculations. 3. (15 pts) Now consider the schematic of the second IF stage in the model AM/FM-108K receiver from p19 of your Assembly manual.
Figure 1.3a Copy of the schematic of the second IF stage of the AM/FM 108K receiver. This stage includes at two resonant LC circuits, since the autotransformers (as represented by parts T7 and T8) are also inductances. Construct this circuit for simulation using pSpice. In place of T7 use the part K502T300_3C8 (which is a Ferrite core autotransformer much like that of T7). You will need to set the number of turns N1 and N2 = 50, [In the pSpice schematic shown (Figure 1.4) this was done parametrically] and set the coupling to parametric value {Kc}, for which you also will need to declare it under the PARAMETER call, with default value Kc = 0.3 (as shown).
Figure 1.3a: Parametric settings and model parameters for the Ferrite core autotransformer In the physical autotransformer, coupling is adjusted by moving the little ferrite slug inside the autotransformer by means of a small (plastic) screwdriver blade. You will do so when building your receiver. In this case you are going to adjust it using pSpice. Autotransformer T8 is replaced with a parallel RLC circuit as shown by figure 1.4. Note that the capacitance and inductance are also parameterized for adjustment of R0 without changing its characteristic frequency f0.
Figure 1.4 pSpice model for the second IF stage. Your completed pSpice schematic will be your figure 1.4a. 4. (10 pts) For the simulation you have need to perform an AC sweep (type: Decade, 1001pts/decade, sweep from 100K to 10Meg), for which you should see a resonance peak somewhere in the neighborhood of 455 kHz, not unlike what you will find in the laboratory setting. Take a snapshot and record it as your Figu...