Microelectronic Circuits II

EE-430 Lab 4

Daniel Hurn

Torry Steed

Ted Young

Title: Feedback

Purpose: This lab combines the differential and voltage gain stages and incorporates a feedback loop into the established two stage amplifier, setting the overall gain to 10X. Estimate changes in the frequency poles and changes in the gain of different stage. Use test equipment to verify estimates. See the rise time of the amplifier and calculate the R_inf.

Theory: Open-loop gains of many amplifier circuits give tremendous magnitudes but are very sensitive, being forced out of the linear region of the transistors being used for the circuit. Operating temperatures can also effect beta's of transistors. The variation of manufacturing cannot guarantee accuracy in performance of transistors. With the use of negative feedback, circuits loose the gain magnitudes, but they get stability and accuracy in operation. Feedback frees circuits of the variations in parts and force circuits to be kept in the linear region of operation.

Measurements and Calculations:

Section 4.2 Series -Shunt Feedback Operation:

Load on the differential stage is effected by the linking of the second stage.

Equation 4-3 states the input resistance of the second stage is:

R_in5 = R_B5 || ( + 1)(r_e5 + R_E5)

R_in5 = 19.9k || (128 * (25 + 220))

R_in5 = 12.17k

Equation 4-2, the modified gain equation of the first stage:

A_d = (R_c4 || R_in5) / (2*r_e4)

A_d = (2.86k || 12.7k) / (2*25)

A_d = 46.3 v/v

Equation 4-4: f_L = 1 / (2 * * C_E5 * (R_E5 + r_e5 + ((R_C4 || R_B5 )/ ( + 1))

f_L = 1 / (2 * * 33.4u * (221 + 25 + ((2.8k || 19.9k) / 128))

Calculation (4-1) f_L = 17.9 Hz, 3dB point = 12.6 Hz

Section 4.3 Closed-loop gain considerations: A_CL

Feedback amplifier gain is shown as follows:

Equation (4-12) G = 1 + R₂ / R₁

G = 1 + 17.72K / 1.9K

G = 10.05

Measurements (4-1) and (4-2) TP1 = .200mV TP2 = 2.00V

Calculation (4-2) GAIN = TP2 / TP1 = 10.00 v/v

Section 4.4 Feedback Frequency Response Considerations:

Measurement (4-3) f_Lf = .6 Hz

Equation 4-5 BETA = R₁ / (R₂ + R₁) = 17.71 / ( 1.916 + 17.71) = .900

Equation 4-7 f_Lf = F_L / (1 + (A_v * BETA)) = 17.9 / (1 + (300 * .9)) = .066

Calculation (4-3) f_Lf = .066

Slew-rate limiting is a distortion induced by an amplifier stage that needs to sink or source more instantaneous current than it can handle. This form of distortion is seen when the maximum signal is seen at peak voltage and frequency. Looking for an output level of 2 V_pp we find the f_max to be as follows:

Calculation (4-4) f_max = I_E5 / (2 * * C_B6 * V_p) = 1mA / (2 * * 1.48nf *1v)

f_max = 107.5 kHz

Measurement (4-4) f_max = 100 kHz (slew rate limited)

Calculating Risetime

Measurement (4-5) t_r = 3 ms

Equation (4-18) t_r = 2.2 *

Estimating the high frequency using rise time.

Equation (4-20) f_hf = .35 / t_r

Calculation (4-5) f_hf = 116.67 kHz

Section 4.5 Feedback Amplifier Input Impedance Considerations:

After modifying the circuit to match figure 4-7, adjust the signal generator frequency to 1kHz with output level of 300mV pp and measure the Test points

Measurement 4-6 TP2 = 300mV

Measurement 4-7 TP1 = 370mV

These measurements can be used to determine input resistance of the feedback circuit.

Calculation 4-6 R_inf = (TP2) * Rs / (TP1 - TP2) = 300 * 100.4 / (370 - 300)

R_inf = 430.3k

Conclusions:

• •In this lab we linked the first two stages of our multistage amplifier together. When connecting these stages the second stage altered the gain of the differential stage because of the load from the second stage input resistance.
• •We also verified the calculated low frequency poles and the high frequency poles through measurements and calculations.
• •With the feedback established, we were able to verify our target gain of 10X.
• •We calculated the rise time of the amplifier and the maximum high frequency pole of the circuit.

This lab really shows how feedback controls the effects of a multi-stage amplifier. Without feedback, we calculated resistor values to get certain gain values and were continuously off in gain by some amount in the actual circuit. With feedback resistors, we were able to control the gain to the exact value we wanted.