rc coupling

Related Concepts: direct coupling

Based on Laboratory Exercise 16: RC Coupling from your manual, here is the revision note.

1) Experiment Snapshot

Experiment Title: RC Coupling (Two-Stage Amplifier)

Objective(s):

Identify a two-stage RC coupled amplifier and measure DC operating voltages.
Measure AC voltage gains of individual stages and the overall cascaded system.
Determine the frequency response of the RC coupled amplifier.

Core Principle / Theory:

Cascading: Connecting the output of one amplifier (Stage 1) to the input of the next (Stage 2) multiplies the individual gains ( $A_{t o t a l} = A_{1} \times A_{2}$ ).
RC Coupling: A capacitor ( $C_{C}$ ) allows AC signals to pass between stages while blocking DC voltages, preventing the DC bias of one stage from upsetting the other.
Loading Effect: The input impedance of the second stage acts as a load on the first stage, reducing the first stage’s effective voltage gain.
Frequency Response: Limited at low frequencies by the reactance of coupling capacitors and at high frequencies by transistor/stray capacitance.

Key Formula(s):

Stage Gain: $A_{V 1} = \frac{e _{c 1}}{e _{i}}$ , $A_{V 2} = \frac{e _{o}}{e _{b 2}}$
Total Gain: $A_{V} = A_{V 1} \times A_{V 2} = \frac{e _{o}}{e _{i}}$
Total Gain (dB): Not explicitly asked, but implied by frequency response plots.

2) Apparatus Setup

Connection / Block Diagram:

Stage 1 (Q1): Common Emitter setup. Output taken from Collector via Capacitor C2.
Coupling: C2 connects Q1 Collector to Q2 Base.
Stage 2 (Q2): Common Emitter setup. Input at Base, Output at Collector via C3.
Power: +24V DC ( $V_{CC}$ ) connected to both stages.
Components: 2x NPN Transistors (2N2219A), Coupling Caps ( $10 μ F$ ), Bypass Caps (optional step).

Precautions:

Capacitor Polarity: Ensure electrolytic capacitors (C1, C2, C3, C4) are connected with the positive terminal towards the more positive DC potential.
Grounding: Connect the grounds of the AF Generator, Oscilloscope, and circuit together.

3) Procedure

Part A: DC Analysis

Connect the two-stage circuit (Fig 16-2). Leave AC source at zero.
Adjust $V_{CC}$ to 24V DC.
Measure DC voltages with respect to ground for both transistors:
- Stage 1: Base ( $V_{B 1}$ ), Emitter ( $V_{E 1}$ ), Collector ( $V_{C 1}$ ).
- Stage 2: Base ( $V_{B 2}$ ), Emitter ( $V_{E 2}$ ), Collector ( $V_{C 2}$ ).
- Check: $V_{B}$ should be ~0.6V higher than $V_{E}$ (Forward Bias).

Part B: AC Gain Measurement 4. Set AF Generator to 1kHz Sine Wave. 5. Adjust input ( $e_{i}$ ) to 100mV pk-pk at Q1 Base. 6. Measure output of Stage 1 ( $e_{c 1}$ ) at Q1 Collector. * Note: This is also the input to Stage 2 ( $e_{b 2}$ ). 7. Measure final output ( $e_{o}$ ) at Q2 Collector. 8. Calculate gains ( $A_{V 1}, A_{V 2}, A_{T o t a l}$ ). 9. Load Test: Connect external load resistor $R 9$ ( $22 k Ω$ ) across output. Measure new $e_{o}$ . 10. Bypass Test: Connect emitter bypass capacitor $C 4$ across $R 8$ (Stage 2 emitter resistor). Measure new $e_{o}$ .

Part C: Frequency Response 11. Remove bypass capacitor C4 (restore to original). 12. Sweep frequency from 20Hz to 100kHz (refer to Table 16-1). 13. Maintain constant input voltage (100mV pk-pk) at every step. 14. Measure and record output voltage ( $e_{o}$ ) for each frequency.

4) Data Taken / Measurements

Table 1: DC Operation

Parameter	Stage 1 (Q1)	Stage 2 (Q2)	Unit
Base Voltage ( $V_{B}$ )	~1.5	~1.5	Vdc
Emitter Voltage ( $V_{E}$ )	~0.9	~0.9	Vdc
Collector Voltage ( $V_{C}$ )	~15.0	~15.0	Vdc

Table 2: AC Gain (1kHz, 100mV Input)

Measurement	Value	Unit	Calculation
Stage 1 Output ( $e_{c 1}$ )	~0.4 - 0.5	$V_{pp}$	$A_{V 1} \approx 4 - 5$
Stage 2 Output ( $e_{o}$ )	~3.5 - 4.5	$V_{pp}$	$A_{V 2} \approx 8 - 10$
Total Output	~4.0	$V_{pp}$	$A_{T o t a l} \approx 35 - 45$

Table 3: Frequency Response (Sample)

Frequency	Input ( $e_{i}$ )	Output ( $e_{o}$ )
20 Hz	100mV	(Lower)
1 kHz	100mV	(Max/Flat)
100 kHz	100mV	(Lower)

5) Calculations / Graphs

Gain Calculation:

$A_{V 1} = \frac{e _{c 1}}{e _{i}} = \frac{0.425 V}{0.1 V} = 4.25$ (Example)
$A_{V 2} = \frac{e _{o}}{e _{c 1}} = \frac{4 V}{0.425 V} \approx 9.4$
$A_{T o t a l} = A_{V 1} \times A_{V 2} = 4.25 \times 9.4 \approx 40$

Graph:

Plot: Frequency (Log Scale, X-axis) vs Output Voltage (Linear Scale, Y-axis).
Shape: “Flat” top in the audio range (100Hz – 20kHz). Rolls off (drops) at very low (<50Hz) and very high (>50kHz) frequencies.

6) Results & Outcome

Biasing: Both stages are identically biased ( $V_{C} \approx 15 V$ , $V_{E} \approx 0.9 V$ ).
Gain: The total gain ( $\approx 40$ ) is the product of the two individual stage gains.
- Note: Stage 1 gain is lower than a standalone CE amp because Stage 2 loads it down.
Frequency Response: The amplifier provides flat gain across the audio spectrum (20Hz–20kHz) but drops at the extremes.
Phase: Each stage inverts by 180°. Two stages result in $180° + 180° = 360°$ (or 0°), so the final output is in phase with the input.

7) Why This Outcome Happens (Reasoning)

Reduced Stage 1 Gain: The effective load on Stage 1 is its own Collector Resistor ( $R 3$ ) in parallel with the Input Impedance of Stage 2 ( $R 5∣∣ R 6∣∣ β R_{E 2}$ ). This lowers the effective AC resistance, lowering the gain ( $A_{V} \approx R_{L o a d} / R_{E}$ ).
Frequency Drop-off:
- Low Freq: Coupling capacitors ( $C 1, C 2, C 3$ ) have high reactance ( $X_{C} = \frac{1}{2 π f C}$ ), blocking the signal.
- High Freq: Transistor internal capacitance and stray wiring capacitance shunt the signal to ground.
Emitter Bypass (C4): When added, C4 shorts the emitter resistor $R 8$ for AC signals, removing negative feedback and drastically increasing the gain of Stage 2.

8) Viva / Lab Test Quick Prep

Q1: What is the main advantage of cascading amplifiers? A: To obtain a higher overall voltage gain ( $A_{T o t a l} = A_{1} \times A_{2}$ ).

Q2: What is the purpose of the coupling capacitor $C_{C}$ ? A: To pass AC signals between stages while blocking DC, preventing bias interference.

Q3: Why is the gain of the first stage lower than expected? A: Because of the “loading effect”—the input impedance of the second stage acts as a load on the first stage, reducing its effective output resistance.

Q4: What happens to the bandwidth if we use RC coupling? A: It is generally suitable for audio frequencies but limited at low frequencies by the coupling capacitor reactance.

Q5: What is the phase relationship of the total output vs input? A: In-phase. Stage 1 inverts (180°), Stage 2 inverts again (180°), returning to 0°.

Q6: Why does gain drop at low frequencies? A: Reactance of coupling capacitors increases, dropping more signal voltage across them instead of the load.

Common Mistakes:

Polarity: Exploding capacitors by reversing polarity (C2 connects collector +15V to Base +1.5V, so + side faces collector).
Ground loops: Not connecting the generator ground to the circuit ground, causing noise or no signal.

007_index