CMRR
and
AC VOLTMETERS
OUTLINE
• CMRR
• General structure of AC voltmeters
• Peak voltmeter
• Peak-to-peak voltmeter
• Average value voltmeter
CMRR
Case a)
Common mode voltage as input
• 𝐶𝑜𝑚𝑚𝑜𝑛 𝑚𝑜𝑑𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒, 𝑉𝑐𝑚 =
𝑉𝐴 +𝑉𝐵
2
Case b)
Different reference voltages
Case b)
Different reference voltages
Since 𝑍𝑖 ≫ 𝑅𝑐𝑚
(Normal mode voltage)
Case b)
Different reference voltages
• Solution: 𝑺𝒉𝒊𝒆𝒍𝒅𝒊𝒏𝒈
Case b)
Different reference voltages
• Solution: 𝑫𝒐𝒖𝒃𝒍𝒆 𝑺𝒉𝒊𝒆𝒍𝒅𝒊𝒏𝒈
General structure of AC voltmeters
General structure of AC voltmeters
• AC/DC converter
• Digital (DC) voltmeter
Peak voltmeter
Peak voltmeter
Vx > Vout  the capacity is charged
Vx < Vout  the capacity is discharged
Peak voltmeter
Vx > Vout  time constant tchg is
(ron||R)C ≈ ron C
Vx < Vout  time constant tdchg is
(rOFF||R)C ≈ RC
Ideal diode  ron=0, roff =∞
Peak voltmeter
Vc1 is Vout with an ideal diode
Peak voltmeter
• To reduce oscillations, we reduce the
speed of discharge of C.
• With a ideal voltmeter (R = ∞), and
neglecting other dissipation effects we
would have
Vpeak = Vout
Peak voltmeter
Also named DC-coupled peak voltmeter
AC-coupled peak voltmeter
• At regime, under ideal conditions, Vc is equal
to the maximum of Vx.
• Vout = Vx – Vc 
Vout is a sinusoid
mean (|Vout |) = Vp
AC-coupled peak voltmeter
Peak-to-peak voltmeter
Peak-to-peak voltmeter
• The cascading of the two solutions for DCand AC-coupled peak measurements.
• Let us suppose Vx is a sinusoid with a VDC
superimposed on it.
Peak-to-peak voltmeter
• Let us assume:
• Ideal diodes and voltmeters;
• AC-coupling has settling time << than the
other section.
• Vd is a sinusoid:
• max |Vd| = Vpp;
• Vd is the input to the cascaded DC-coupled
peak voltmeter;
• |Vout| on C1 is equal to Vpp.
Peak-to-peak voltmeter
Peak-to-peak voltmeter
• D1 has opposite polarity with respect to the
DC-coupled peak voltmeter seen before.
• The time constant for the charging of C1 must
be << of that of C.
Average value voltmeter
Average value voltmeter
• Average value voltmeters measure the
average absolute value of the periodic
voltage input:
1
Vm 
T

T
v (t ) dt
• The signal v(t) is rectified.
• The average value of the rectified signal is
measured.
Average value voltmeter
Half-wave rectifier
• If D is ideal:
o Vi > 0  Vu = Vi
o Vi < 0  Vu = 0 (there is no current in R)
Average value voltmeter
Full-wave rectifier (Graëtz bridge)
• Vi > 0  D1–R–D4
• Vi < 0  D2–R–D3
• Current in R doesn’t change polarity.
Result in terms of rms value
• AC voltmeters usually express their result in
term of the rms value Vrms.
• For sinusoidal signals Vrms can be calculated
from Vp, Vpp, Vm as
Vrms 
Vp
2
Vrms 
Vpp
2 2
Vrms 
 Vm
2 2
• For non-sinusoidal signals such relations do
not hold.